A217576 - OEIS

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

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OFFSET

1,2

LINKS

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

FORMULA

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

MATHEMATICA

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

PROG

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

CROSSREFS

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

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

Sequence in context: A333392 A358389 A358279 * A173280 A141477 A211371

Adjacent sequences: A217573 A217574 A217575 * A217577 A217578 A217579

KEYWORD

nonn

AUTHOR

Joerg Arndt, Oct 07 2012

STATUS

approved