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A107758 (+2)Sigma(n): If n=Product p_i^r_i then (+2)Sigma(n)=Product (2+Sum p_i^s_i, s_i=1 to r_i)=Product(1+(p_i^(r_i+1)-1)/(p_i-1)), (+2)Sigma(1)=1. 2
1, 4, 5, 8, 7, 20, 9, 16, 14, 28, 13, 40, 15, 36, 35, 32, 19, 56, 21, 56, 45, 52, 25, 80, 32, 60, 41, 72, 31, 140, 33, 64, 65, 76, 63, 112, 39, 84, 75, 112, 43, 180, 45, 104, 98, 100, 49, 160, 58, 128, 95, 120, 55, 164 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Daniel Suteu, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = Sum_{d|n, gcd(n/d, d) = 1} sigma(d), where sigma(d) is the sum of the divisors of d. - Daniel Suteu, Jun 27 2018

EXAMPLE

(+2)Sigma(6)=(2+2)*(2+3)=20.

MAPLE

A107758 := proc(n) local pf, p ; if n = 1 then 1; else pf := ifactors(n)[2] ; mul( 1+(op(1, p)^(op(2, p)+1)-1)/(op(1, p)-1), p=pf) ; end if; end proc:

seq(A107758(n), n=1..60) ; # R. J. Mathar, Jan 07 2011

MATHEMATICA

Table[DivisorSum[n, DivisorSigma[1, #] &, CoprimeQ[n/#, #] &], {n, 54}] (* Michael De Vlieger, Jun 27 2018 *)

PROG

(PARI) a(n) = sumdiv(n, d, if(gcd(n/d, d) == 1, sigma(d))); \\ Daniel Suteu, Jun 27 2018

CROSSREFS

Cf. A000203, A107759, A052396.

Sequence in context: A020804 A021222 A132023 * A104883 A154885 A292192

Adjacent sequences:  A107755 A107756 A107757 * A107759 A107760 A107761

KEYWORD

nonn,mult

AUTHOR

Yasutoshi Kohmoto, May 25 2005

STATUS

approved

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Last modified January 21 11:09 EST 2020. Contains 331105 sequences. (Running on oeis4.)