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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

%I

%S 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,

%T 60,41,72,31,140,33,64,65,76,63,112,39,84,75,112,43,180,45,104,98,100,

%U 49,160,58,128,95,120,55,164

%N (+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.

%H Daniel Suteu, <a href="/A107758/b107758.txt">Table of n, a(n) for n = 1..10000</a>

%F 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

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

%p 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:

%p seq(A107758(n),n=1..60) ; # _R. J. Mathar_, Jan 07 2011

%t Table[DivisorSum[n, DivisorSigma[1, #] &, CoprimeQ[n/#, #] &], {n, 54}] (* _Michael De Vlieger_, Jun 27 2018 *)

%o (PARI) a(n) = sumdiv(n, d, if(gcd(n/d, d) == 1, sigma(d))); \\ _Daniel Suteu_, Jun 27 2018

%Y Cf. A000203, A107759, A052396.

%K nonn,mult

%O 1,2

%A _Yasutoshi Kohmoto_, May 25 2005

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Last modified February 25 20:04 EST 2020. Contains 332258 sequences. (Running on oeis4.)