A217576 a(n) = Sum_{d divides n} (d!)^(n/d).

1, 3, 7, 29, 121, 765, 5041, 40913, 363097, 3643233, 39916801, 479535185, 6227020801, 87203692929, 1307676103777, 20924415922433, 355687428096001, 6402505760917569, 121645100408832001, 2432915176581403649, 51090942299733783937, 1124002321128529922049

Offset: 1

Author

Joerg Arndt, Oct 07 2012

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..449

Crossrefs

Cf. A062363 ( Sum_{d divides n} d! ).

Cf. A062796 ( Sum_{d divides n} d^d ), A066108 ( Sum_{d divides n} n^d ).

Programs

Mathematica

f[n_]=With[{d=Divisors[n]},Total[(d!)^(n/d)]]; Array[f,25] (* Harvey P. Dale, Dec 20 2023 *)

PARI

a(n)=sumdiv(n,d, (d!)^(n/d) );

Formula

G.f.: Sum_{n>=1} n!*x^n / (1 - n!*x^n). - Paul D. Hanna, Jan 17 2013