1,2

Also sum of divisors of the square-free kernel of n: a(n)=A000203(A007947(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 19 2002

D. Suryanarayana, On the core of an integer, Indian J. Math. 14 (1972) 65-74.

T. D. Noe, Table of n, a(n) for n=1..10000

S. R. Finch, Unitarism and infinitarism.

Index entries for sequences related to sums of squares

If n = Product p_i^e_i, a(n) = Product (p_i + 1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 19 2001

Dirichlet g.f.: zeta(s)*zeta(s-1)/zeta(2*s-2). - Michael Somos, Sep 08, 2002.

a(n)=sum(dIn, mu(d)^2*d) - Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 09 2002

Pieter Moree (moree(AT)science.uva.nl), Feb 20, 2004 can show that Sum_{n <= x} a(n) = x^2/2 + O(x*sqrt{x}) and adds: "As S. R. Finch pointed out to me, in Suryanarayana's paper this is proved under the Riemann hypothesis with error term O(x^{7/5+\epsilon})".

For n=1000 out of the 16 divisors four are square-free: {1,2,5,10}. Their sum is 18. Or, 1000=2^3*5^3 hence a(1000)=(2+1)*(5+1)=18.

A048250 := proc(n) local ans, i:ans := 1: for i from 1 to nops(ifactors(n)[ 2 ]) do ans := ans*(1+ifactors(n)[ 2 ][ i ] [ 1 ]): od: RETURN(ans) end:

sumOfSquareFreeDivisors[ n_ ] := Plus @@ Select[ Divisors[ n ], MoebiusMu[ # ] != 0 & ]; Table[ sumOfSquareFreeDivisors[ i ], {i, 85} ]

(PARI) a(n)=if(n<1, 0, sumdiv(n, d, if(core(d)==d, d)))

(PARI) a(n)=if(n<1, 0, direuler(p=2, n, (1+p*X)/(1-X))[n])

Cf. A034444, A034448, A007947, A003557, A023900.

Sequence in context: A049276 A101684 A061800 this_sequence A073181 A046897 A109506

Adjacent sequences: A048247 A048248 A048249 this_sequence A048251 A048252 A048253

nonn,easy,nice,mult

Labos E. (labos(AT)ana.sote.hu)