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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.
9
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
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
KEYWORD
nonn,easy
AUTHOR
Jianing Song, Apr 05 2021
STATUS
approved