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

Author

Jianing Song, Apr 05 2021

Keywords

• nonn
• easy

Comments

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

Examples

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

Links

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

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.

Programs

Mathematica

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

PARI

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