A095001 a(n) = Sum_{d|n} rad(d)^(n/d), where rad(d) = A007947(d) is the squarefree kernel of d.

1, 3, 4, 7, 6, 24, 8, 23, 31, 68, 12, 196, 14, 192, 384, 279, 18, 1473, 20, 1792, 2552, 2192, 24, 12068, 3131, 8388, 19714, 19124, 30, 116474, 32, 65815, 178512, 131396, 94968, 841093, 38, 524688, 1596560, 1450368, 42, 7280934, 44, 4211500, 16305666

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..6287

Formula

G.f. satisfies: A(x) = Sum_{n>=1} [1/(1-A007947(n)*x^n) - 1].

a(n) = Sum_{d|n} A007947(d)^(n/d); a(p) = p+1, for prime p.

Mathematica

rad[n_] := Times @@ FactorInteger[n][[;; , 1]]; a[n_] := DivisorSum[n, rad[#]^(n / #) &]; Array[a, 50] (* Amiram Eldar, Sep 07 2020 *)

Prog

(PARI) {a(n)=sumdiv(n, d, prod(i=1, omega(d), factor(d)[i, 1])^(n/d))} /* also formed by the log of G094947(x): */ {a(n)=n*polcoeff(sum(k=1, n, -log(1-prod(i=1, omega(k), factor(k)[i, 1])*x^k+x*O(x^n))/k), n)}

Crossrefs

Cf. A007947, A094947.

Sequence in context: A130700 A117134 A334127 * A377378 A344458 A068905

Adjacent sequences: A094998 A094999 A095000 * A095002 A095003 A095004

Keyword

nonn

Author

Paul D. Hanna, May 26 2004

Status

approved