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A211780 a(n) = Sum_{d_<n | n} (d_<n) * tau(n / d_<n), where d_<n = divisors of n that are less than n, tau(x) = A000005(x). 3
0, 2, 2, 7, 2, 14, 2, 18, 9, 18, 2, 43, 2, 22, 20, 41, 2, 54, 2, 57, 24, 30, 2, 106, 13, 34, 31, 71, 2, 110, 2, 88, 32, 42, 28, 162, 2, 46, 36, 142, 2, 138, 2, 99, 81, 54, 2, 237, 17, 102, 44, 113, 2, 178, 36, 178, 48, 66, 2, 325, 2, 70, 99, 183, 40, 194, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers n such that n divides a(n) are given in A068978.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..27144 (first 1000 terms from Jaroslav Krizek)

FORMULA

a(n) = A007429(n) - n = A211779(n) + A000203(n) - n .

a(n) = (Sum_{d|n} A000203(d)) - n. - Antti Karttunen, Nov 13 2017

EXAMPLE

For n = 12: Sum_{d_<n | n} (d_<n) * tau(n / d_<n), = 1*6 + 2*4 + 3*3 + 4*2 + 6*2 = 43.

MAPLE

with(numtheory);

A211780:= proc(q)

local b, d, j, n;

for n from 1 to q do

  b:=divisors(n); d:=add(b[j]*tau(n/b[j]), j=1..nops(b))-n;

  if trunc(d)=d then print(d);

fi; od; end:

A211780(10000); # Paolo P. Lava, Feb 01 2013

MATHEMATICA

Table[Sum[d*DivisorSigma[0, n/d], {d, Most[Divisors[n]]}], {n, 100}] (* T. D. Noe, Apr 27 2012 *)

PROG

(PARI) A211780(n) = (sumdiv(n, d, sigma(d))-n); \\ Antti Karttunen, Nov 13 2017

CROSSREFS

Cf. A000203, A007429, A068978, A211779.

Sequence in context: A029632 A089588 A325211 * A014840 A218756 A317329

Adjacent sequences:  A211777 A211778 A211779 * A211781 A211782 A211783

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Apr 20 2012

STATUS

approved

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Last modified January 28 00:32 EST 2020. Contains 331313 sequences. (Running on oeis4.)