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 A018783 Number of partitions of n into parts having a common factor. 57
 0, 0, 1, 1, 2, 1, 4, 1, 5, 3, 8, 1, 14, 1, 16, 9, 22, 1, 38, 1, 45, 17, 57, 1, 94, 7, 102, 30, 138, 1, 218, 1, 231, 58, 298, 21, 451, 1, 491, 103, 644, 1, 919, 1, 1005, 203, 1256, 1, 1784, 15, 1993, 299, 2439, 1, 3365, 62, 3735, 492, 4566, 1, 6252, 1, 6843, 819, 8349, 107, 11096 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 L. Naughton, G. Pfeiffer, Integer Sequences Realized by the Subgroup Pattern of the Symmetric Group, J. Int. Seq. 16 (2013) #13.5.8 FORMULA a(n) = -Sum_{d|n, d `if`(n=0, 0, numbpart(n) -add(mobius(n/d)*numbpart(d), d=divisors(n))): seq(a(n), n=0..100); # Alois P. Heinz, Nov 29 2011 MATHEMATICA A000837[n_] := Sum[ MoebiusMu[n/d]*PartitionsP[d], {d, Divisors[n]}]; a[0] = 0; a[n_] := PartitionsP[n] - A000837[n]; Table[a[n], {n, 0, 66}] (* Jean-François Alcover, Oct 03 2013, after Vladeta Jovovic *) PROG (PARI) a(n) = - sumdiv(n, d, (d

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Last modified December 9 17:46 EST 2022. Contains 358703 sequences. (Running on oeis4.)