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A023893 Number of partitions of n into prime power parts (1 included); number of nonisomorphic Abelian subgroups of symmetric group S_n. 31
1, 1, 2, 3, 5, 7, 10, 14, 20, 27, 36, 48, 63, 82, 105, 134, 171, 215, 269, 335, 415, 511, 626, 764, 929, 1125, 1356, 1631, 1953, 2333, 2776, 3296, 3903, 4608, 5427, 6377, 7476, 8744, 10205, 11886, 13818, 16032, 18565, 21463, 24768, 28536 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Index entries for sequences related to groups

FORMULA

G.f.: (Product_{p prime} Product_{k>=1} 1/(1-x^(p^k))) / (1-x).

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], Count[Map[Length, FactorInteger[#]], 1] == Length[#] &]], {n, 0, 35}] (* Geoffrey Critzer, Oct 25 2015 *)

nmax = 50; Clear[P]; P[m_] := P[m] = Product[Product[1/(1-x^(p^k)), {k, 1, m}], {p, Prime[Range[PrimePi[nmax]]]}]/(1-x)+O[x]^nmax // CoefficientList[ #, x]&; P[1]; P[m=2]; While[P[m] != P[m-1], m++]; P[m] (* Jean-François Alcover, Aug 31 2016 *)

PROG

(PARI) lista(m) = {x = t + t*O(t^m); gf = prod(k=1, m, if (isprimepower(k), 1/(1-x^k), 1))/(1-x); for (n=0, m, print1(polcoeff(gf, n, t), ", ")); } \\ Michel Marcus, Mar 09 2013

CROSSREFS

Cf. A009490, A023894 (first differences), A062297 (number of Abelian subgroups).

Cf. A000961, A018819, A062051, A131995.

Sequence in context: A116634 A035960 A288254 * A065094 A145728 A145786

Adjacent sequences:  A023890 A023891 A023892 * A023894 A023895 A023896

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified August 14 18:32 EDT 2020. Contains 336483 sequences. (Running on oeis4.)