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A074754 Number of integers k such that sigma(k) divides n. 2
1, 1, 2, 2, 1, 3, 2, 3, 2, 1, 1, 6, 2, 3, 3, 3, 1, 5, 1, 3, 3, 1, 1, 10, 1, 2, 2, 5, 1, 5, 3, 5, 2, 1, 2, 9, 1, 2, 4, 5, 1, 8, 1, 3, 3, 1, 1, 13, 2, 1, 2, 3, 1, 7, 1, 8, 3, 1, 1, 12, 1, 4, 4, 5, 2, 3, 1, 3, 2, 3, 1, 18, 1, 2, 3, 3, 2, 6, 1, 7, 2, 1, 1, 15, 1, 1, 2, 4, 1, 10, 4, 2, 5, 1, 1, 19, 1, 5, 2, 3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences related to sigma(n)

FORMULA

sum(k=1, n, a(k)) seems to be asymptotic to c*n*log(n) with c=0.7...

G.f.: sum(k>=1, 1/(1-x^sigma(k)))

MATHEMATICA

Table[Length[Select[Range[n], Divisible[n, DivisorSigma[1, #]]&]], {n, 1, 100}] (* Vaclav Kotesovec, Feb 16 2019 *)

PROG

(PARI) a(n)=sum(i=1, n, if(n%sigma(i), 0, 1))

(PARI) a(n)=if(n<1, 0, polcoeff(sum(k=1, n, 1/(1-x^sigma(k)), x*O(x^sigma(n))), n))

CROSSREFS

Cf. A000203, A070610.

Sequence in context: A241605 A128180 A209279 * A322529 A329949 A333867

Adjacent sequences:  A074751 A074752 A074753 * A074755 A074756 A074757

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Sep 28 2002

STATUS

approved

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Last modified October 15 21:38 EDT 2021. Contains 348034 sequences. (Running on oeis4.)