A343111 Numbers having exactly 2 divisors of the form 8*k + 1, that is, numbers with exactly 1 divisor of the form 8*k + 1 other than 1.

9, 17, 18, 25, 27, 33, 34, 36, 41, 45, 49, 50, 51, 54, 57, 63, 65, 66, 68, 72, 73, 75, 82, 85, 89, 90, 97, 98, 100, 102, 105, 108, 113, 114, 117, 119, 121, 123, 125, 126, 129, 130, 132, 135, 136, 137, 144, 145, 146, 147, 150, 161, 164, 165, 169, 170, 175

Offset

1,1

Links

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

Example

63 is a term since among the divisors of 63 (namely 1, 3, 7, 9, 21 and 63), the only divisors congruent to 1 modulo 8 are 1 and 9.

Prog

(PARI) res(n, a, b) = sumdiv(n, d, (d%a) == b)
isA343111(n) = (res(n, 8, 1) == 2)

Crossrefs

Numbers having m divisors of the form 8*k + i: A343107 (m=1, i=1), A343108 (m=0, i=3), A343109 (m=0, i=5), A343110 (m=0, i=7), this sequence (m=2, i=1), A343112 (m=1, i=3), A343113 (m=1, i=5), A141164 (m=1, i=7).

Indices of 2 in A188169.

A007519 is a subsequence.

Sequence in context: A134104 A124966 A224442 * A364540 A347250 A192049

Adjacent sequences: A343108 A343109 A343110 * A343112 A343113 A343114

Keyword

nonn,easy

Author

Jianing Song, Apr 05 2021

Status

approved