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 A352058 a(n) = Sum_{p|n, p prime} n!/(p!*(n/p)!). 2
 0, 1, 1, 6, 1, 120, 1, 840, 10080, 30240, 1, 3659040, 1, 17297280, 3632428800, 259459200, 1, 1490852563200, 1, 845092863014400, 3379030566912000, 28158588057600, 1, 2565331847811532800, 1077167364120207360000, 64764752532480000, 5001134190558105600000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Table of n, a(n) for n=1..27. FORMULA E.g.f.: Sum_{p prime} (exp(x^p) - 1)/p!. a(n) = 1 if and only if n is prime. MATHEMATICA a[1] = 0; a[n_] := Plus @@ (n!/((p=FactorInteger[n][[;; , 1]])!*(n/p)!)); Array[a, 30] (* Amiram Eldar, Mar 02 2022 *) PROG (PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, n!/(f[k, 1]!*(n/f[k, 1])!)); (PARI) my(N=40, x='x+O('x^N)); concat(0, Vec(serlaplace(sum(k=1, N, isprime(k)*(exp(x^k)-1)/k!)))) CROSSREFS Cf. A121860, A352012, A352059, A352060. Sequence in context: A318107 A365908 A331557 * A303675 A266302 A352012 Adjacent sequences: A352055 A352056 A352057 * A352059 A352060 A352061 KEYWORD nonn AUTHOR Seiichi Manyama, Mar 02 2022 STATUS approved

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Last modified April 23 16:40 EDT 2024. Contains 371916 sequences. (Running on oeis4.)