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A173441 Number of divisors d of n such that sigma(d) divides n. 8
1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 1, 5, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

From Robert Israel, Oct 11 2017: (Start)

a(n) >= 1 since d=1 is always included.

a(n) = 1 if n is in A000961.

a(n) > 1 if n is in A097603.  The first n not in A097603 such that a(n) > 1 is 117. (End)

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A000005(n) - A173442(n). - A-number inserted by R. J. Mathar, Mar 06 2010

EXAMPLE

For n = 12, a(12) = 4; divisors of 12: 1, 2, 3, 4, 6, 12; corresponding sigma(d):1, 3, 4, 7, 12, 28; sigma(d) divides n for 4 divisors d: 1, 2, 3, 6.

MAPLE

f:= proc(n) nops(select(t -> n mod numtheory:-sigma(t) = 0, numtheory:-divisors(n))) end proc:

map(f, [$1..100]); # Robert Israel, Oct 11 2017

MATHEMATICA

a[n_] := Select[Divisors[n], Divisible[n, DivisorSigma[1, #]]&] // Length;

Array[a, 100] (* Jean-Fran├žois Alcover, Jun 05 2020 *)

PROG

(PARI) a(n) = sumdiv(n, d, !(n % sigma(d))); \\ Michel Marcus, Oct 11 2017

CROSSREFS

Cf. A000005, A000961, A097603, A173442.

Sequence in context: A010248 A325403 A132068 * A326851 A129192 A062540

Adjacent sequences:  A173438 A173439 A173440 * A173442 A173443 A173444

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Feb 18 2010

STATUS

approved

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Last modified November 23 14:26 EST 2020. Contains 338590 sequences. (Running on oeis4.)