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A173442 Number of divisors d of number n such that sigma(d) does not divide n. 2
0, 1, 1, 2, 1, 2, 1, 3, 2, 3, 1, 2, 1, 3, 3, 4, 1, 4, 1, 5, 3, 3, 1, 4, 2, 3, 3, 4, 1, 5, 1, 5, 3, 3, 3, 5, 1, 3, 3, 7, 1, 6, 1, 5, 5, 3, 1, 6, 2, 5, 3, 5, 1, 6, 3, 4, 3, 3, 1, 7, 1, 3, 5, 6, 3, 6, 1, 5, 3, 7, 1, 8, 1, 3, 5, 5, 3, 6, 1, 9, 4, 3, 1, 6, 3, 3, 3, 7, 1, 8, 3, 5, 3, 3, 3, 8, 1, 5, 5, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Sigma(n) = A000203(n). a(n) = A000005(n) - A173441(n).

a(n) >= 1 for n >= 2, with equality if and only if n is prime. - Robert Israel, Oct 10 2017

LINKS

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

EXAMPLE

For n = 12, a(12) = 2. We see that the divisors of 12 are 1, 2, 3, 4, 6, 12. The corresponding sigma(d) are 1, 3, 4, 7, 12, 28. The sigma(d) which do not divide n for 2 divisors d are 4 and 12.

MAPLE

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

map(f, [$1..100]); # Robert Israel, Oct 10 2017

MATHEMATICA

Table[Length[Select[Divisors[n], Not[Divisible[n, DivisorSigma[1, #]]], &]], {n, 100}] (* Alonso del Arte, Oct 10 2017 *)

PROG

(PARI) a(n) = sumdiv(n, d, (n % sigma(d)) != 0); \\ Michel Marcus, Oct 11 2017

CROSSREFS

Cf. A000005, A000203, A173441.

Sequence in context: A261350 A259177 A304036 * A112309 A160006 A060682

Adjacent sequences:  A173439 A173440 A173441 * A173443 A173444 A173445

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Feb 18 2010

EXTENSIONS

More terms from Robert Israel, Oct 10 2017

STATUS

approved

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Last modified September 19 11:26 EDT 2019. Contains 327193 sequences. (Running on oeis4.)