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A088725
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Numbers having no divisors d>1 such that also d+1 is a divisor.
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21
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1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91
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OFFSET
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1,2
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COMMENTS
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The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 9, 79, 778, 7782, 77813, 778055, 7780548, 77805234, 778052138, 7780519314, ... . Apparently, the asymptotic density of this sequence exists and equals 0.77805... . - Amiram Eldar, Jun 14 2022
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LINKS
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FORMULA
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EXAMPLE
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The sequence of terms together with their divisors > 1 begins:
1: {}
2: {2}
3: {3}
4: {2,4}
5: {5}
7: {7}
8: {2,4,8}
9: {3,9}
10: {2,5,10}
11: {11}
13: {13}
14: {2,7,14}
15: {3,5,15}
16: {2,4,8,16}
17: {17}
19: {19}
21: {3,7,21}
22: {2,11,22}
23: {23}
25: {5,25}
(End)
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MATHEMATICA
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Select[Range[100], FreeQ[Differences[Rest[Divisors[#]]], 1]&] (* Harvey P. Dale, Sep 16 2017 *)
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PROG
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(PARI) isok(n) = {my(d=setminus(divisors(n), [1])); #setintersect(d, apply(x->x+1, d)) == 0; } \\ Michel Marcus, Oct 28 2019
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CROSSREFS
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Positions of 0's and 1's in A129308.
Positions of 0's and 1's in A328457 (also).
Numbers whose divisors (including 1) have no non-singleton runs are A005408.
The number of runs of divisors of n is A137921(n).
The longest run of divisors of n has length A055874(n).
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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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