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#24 by OEIS Server at Wed Jul 24 21:28:36 EDT 2024
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| LINKS
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Amiram Eldar, <a href="/A063956/b063956_1.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harry J. Smith)
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#23 by Alois P. Heinz at Wed Jul 24 21:28:36 EDT 2024
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Discussion
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| Wed Jul 24
| 21:28
| OEIS Server: Installed new b-file as b063956.txt. Old b-file is now b063956_1.txt.
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#22 by Amiram Eldar at Wed Jul 24 03:24:13 EDT 2024
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#21 by Amiram Eldar at Wed Jul 24 02:38:59 EDT 2024
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| EXAMPLE
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The prime divisors of 420 = 2^2 * 3 * 5 * 7 that have exponent 1 (i.e., unitary prime divisors) are {3, 5, 7}, so a(420)= ) = 3 + 5 + 7 = 15.
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#20 by Amiram Eldar at Wed Jul 24 02:38:19 EDT 2024
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| EXAMPLE
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The prime divisors of 420 = 2^2 * 3 * 5 * 7 that have exponent 1 (i.e., unitary prime divisors) are {3, 5, 7}, so a(420)= 3 + 5 + 7 = 1215.
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#19 by Amiram Eldar at Wed Jul 24 02:36:36 EDT 2024
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| LINKS
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Amiram Eldar, <a href="/A063956/b063956_1.txt">Table of n, a(n) for n = 1..10000</a>> (terms 1..1000 from Harry J. Smith)
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#18 by Amiram Eldar at Wed Jul 24 02:36:24 EDT 2024
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| LINKS
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HarryAmiram J. SmithEldar, <a href="/A063956/b063956_1.txt">Table of n, a(n) for n = 1..100010000</a>
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| KEYWORD
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nonn,easy,changed
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#17 by Amiram Eldar at Wed Jul 24 02:31:52 EDT 2024
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#16 by Amiram Eldar at Wed Jul 24 02:31:34 EDT 2024
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| EXAMPLE
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PrimeThe prime factorsdivisors inof 420 whichthat have exponent= 1 (i.e., unitary prime p-divisors) are {5,7}; sum = 12, 7}, so a(420)=)= 5 + 7 = 12. (The sum of all its p-divisors, unitary and non-unitary, is A008472(420) = 17.).
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#15 by Amiram Eldar at Wed Jul 24 02:29:42 EDT 2024
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| FORMULA
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From Amiram Eldar, Jul 24 2024: (Start)
a(n) = A008472(n) - A063958(n).
Additive with a(p^e) = p is e = 1, and 0 otherwise. (End)
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| MATHEMATICA
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f[p_, e_] := If[e == 1, p, 0]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jul 24 2024 *)
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| CROSSREFS
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Cf. A008472, A034387, A034444, A056169-, A056170, A056171, A056172, A034387A063958.
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| STATUS
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approved
editing
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