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Search: id:A088044
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| A088044 |
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Number of partitions of n with distinct prime signatures. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,3
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EXAMPLE
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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.
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PROGRAM
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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); (Wasserman)
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CROSSREFS
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Cf. A088045.
Sequence in context: A104410 A018048 A077564 this_sequence A029051 A079398 A071988
Adjacent sequences: A088041 A088042 A088043 this_sequence A088045 A088046 A088047
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 20 2003
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Jun 21 2005
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