A088044 Number of partitions of n with distinct prime signatures.
1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 8, 10, 10, 11, 14, 14, 19, 22, 22, 25, 30, 34, 38, 40, 46, 54, 60, 63, 74, 81, 85, 91, 108, 118, 126, 134, 153, 173, 180, 186, 214, 236, 245, 262, 301, 326, 338, 355, 395, 437, 461, 476, 540, 592, 610, 649, 717, 768, 811, 853, 943, 1039, 1078
Offset: 1
Keywords
Examples
a(9) = 6 and the partitions are (9), (1,8), (3,6),(4,5), (1,2,6),(2,3,4). The partitions (2,7), (1,3,5),(1,4,4), etc. are not considered for the count as 2 and 7 both are prime and so on.
Crossrefs
Cf. A088045.
Programs
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PARI
ps(n) = local(f); f = factor(n); vecsort(f[,2]); b(n, lim, used, cUsed) = local(s, v, found, j, used2); if (n == 0, return(1)); if (n > lim*(lim + 1)/2, return(0)); s = 0; for (i = 1, lim, v = ps(i); found = 0; j = 1; while (!found && j <= cUsed, if (v == used[j], found = 1, j++)); if (!found, used2 = used; used2[1 + cUsed] = v; s += b(n - i, min (n - i, i - 1), used2, cUsed + 1))); s; a(n) = b(n, n, vector(12), 0); \\ David Wasserman, Jun 21 2005
Extensions
More terms from David Wasserman, Jun 21 2005
Comments