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A217576
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a(n) = Sum_{d divides n} (d!)^(n/d).
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4
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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
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1,2
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LINKS
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FORMULA
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G.f.: Sum_{n>=1} n!*x^n / (1 - n!*x^n). - Paul D. Hanna, Jan 17 2013
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MATHEMATICA
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f[n_]=With[{d=Divisors[n]}, Total[(d!)^(n/d)]]; Array[f, 25] (* Harvey P. Dale, Dec 20 2023 *)
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PROG
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(PARI) a(n)=sumdiv(n, d, (d!)^(n/d) );
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CROSSREFS
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Cf. A062363 ( Sum_{d divides n} d! ).
Cf. A062796 ( Sum_{d divides n} d^d ), A066108 ( Sum_{d divides n} n^d ).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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