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A125088
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a(1)=1. a(n) = sum of the earlier terms equal to any exponent in the prime-factorization of n.
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2
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1, 1, 2, 2, 2, 2, 2, 0, 10, 2, 2, 16, 2, 2, 2, 0, 2, 24, 2, 26, 2, 2, 2, 2, 32, 2, 0, 36, 2, 2, 2, 0, 2, 2, 2, 46, 2, 2, 2, 2, 2, 2, 2, 62, 62, 2, 2, 2, 66, 68, 2, 70, 2, 2, 2, 2, 2, 2, 2, 84, 2, 2, 88, 0, 2, 2, 2, 94, 2, 2, 2, 98, 2, 2, 104, 104, 2, 2, 2, 2, 0, 2, 2, 116, 2, 2, 2, 2, 2, 126, 2, 128
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OFFSET
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1,3
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COMMENTS
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Only a(1) and a(2) are odd. a(n)=0 for n>1 in A036966.
Only possible values: ..., 0, 1, 2, 10, 16, 24, 26, 32, 36, 46, 62, 66, 68, 70, 84, 88, 94, 98, 104, ..., .
Position of first occurrence: 8, 1, 3, 9, 12, 18, 20, 25, 28, 36, 44, 49, 50, 52, 60, 63, 68, 72, 75, ..., .
(End)
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LINKS
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EXAMPLE
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12 has a prime factorization of 2^2 *3^1. So a(12) is the sum of the terms among the first 11 terms of the sequence which equal 1 or 2. There are seven 2's and two 1's among the first 11 terms; so a(12) = 1+1+2+2+2+2+2+2+2 = 16.
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MATHEMATICA
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f[l_List] := Append[l, Plus @@ Select[l, MemberQ[Last /@ FactorInteger[Length[l] + 1], # ] &]]; Nest[f, {1}, 91] (* Ray Chandler, Nov 21 2006 *)
a[1] = 1; a[n_] := a[n] = Plus @@ Flatten[ Cases[ Array[a, n - 1], # ] & /@ Union@ Last@ Transpose@ FactorInteger@n]; Array[a, 92] (* Robert G. Wilson v, Nov 22 2006 *)
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PROG
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(PARI)
up_to = 105;
A125088list(up_to) = { my(v=vector(up_to)); v[1] = 1; for(n=2, up_to, my(es = vecsort(factor(n)[, 2], , 8)); v[n] = sum(k=1, n-1, v[k]*!!vecsearch(es, v[k]))); (v); };
v125088 = A125088list(up_to);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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