A343107 Numbers having exactly 1 divisor of the form 8*k + 1, that is, numbers with no divisor of the form 8*k + 1 other than 1.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 19, 20, 21, 22, 23, 24, 26, 28, 29, 30, 31, 32, 35, 37, 38, 39, 40, 42, 43, 44, 46, 47, 48, 52, 53, 55, 56, 58, 59, 60, 61, 62, 64, 67, 69, 70, 71, 74, 76, 77, 78, 79, 80, 83, 84, 86, 87, 88, 91, 92, 93, 94, 95, 96

Offset

1,2

Comments

Numbers not divisible by at least one of 9, 17, 25, ...

Links

Jianing Song, Table of n, a(n) for n = 1..10000

Example

7 is a term since it has no divisor congruent to 1 modulo 8 other than 1.

Mathematica

Select[Range[100], NoneTrue[Rest[Divisors[#]], Mod[#, 8]==1&]&] (* Harvey P. Dale, Jun 01 2022 *)

Prog

(PARI) res(n, a, b) = sumdiv(n, d, (d%a) == b)
isA343107(n) = (res(n, 8, 1) == 1)

Crossrefs

Numbers having m divisors of the form 8*k + i: this sequence (m=1, i=1), A343108 (m=0, i=3), A343109 (m=0, i=5), A343110 (m=0, i=7), A343111 (m=2, i=1), A343112 (m=1, i=3), A343113 (m=1, i=5), A141164 (m=1, i=7).

Indices of 1 in A188169.

Sequence in context: A191845 A274375 A364542 * A004745 A158037 A332109

Adjacent sequences: A343104 A343105 A343106 * A343108 A343109 A343110

Keyword

nonn,easy

Author

Jianing Song, Apr 05 2021

Status

approved