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A188171 The number of divisors d of n of the form d == 5 (mod 8). 10
0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 2, 0, 1, 0, 0, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,45

COMMENTS

a(5n) >=1 as d=5 contributes to the count.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

M. D. Hirschhorn, The number of representations of a number by various forms, Discrete Mathematics 298 (2005), 205-211.

FORMULA

A188169(n)+a(n) = A001826(n).

A188169(n)+A188170(n)-a(n)-A188172(n) = A002325(n).

G.f.: Sum_{k>=1} x^(5*k)/(1 - x^(8*k)). - Ilya Gutkovskiy, Sep 11 2019

EXAMPLE

a(13) = 1 because the divisor d=13 is 8+5 == 5 (mod 8).

MAPLE

sigmamr := proc(n, m, r) local a, d ; a := 0 ; for d in numtheory[divisors](n) do if modp(d, m) = r then a := a+1 ; end if; end do: a; end proc:

A188171 := proc(n) sigmamr(n, 8, 5) ; end proc:

PROG

(PARI) A188171(n) = sumdiv(n, d, (5==(d%8)));  \\ Antti Karttunen, Jul 09 2017

CROSSREFS

Cf. A001826, A002325, A188169, A188170, A188172.

Sequence in context: A242830 A101668 A141846 * A330733 A328496 A035202

Adjacent sequences:  A188168 A188169 A188170 * A188172 A188173 A188174

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, Mar 23 2011

STATUS

approved

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Last modified July 31 05:39 EDT 2021. Contains 346367 sequences. (Running on oeis4.)