A088045 -id:A088045

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A088044

Number of partitions of n with distinct prime signatures.

+10
1

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

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OFFSET

1,3

COMMENTS

Essentially the same as A077564. [From R. J. Mathar, Sep 11 2008]

LINKS

Table of n, a(n) for n=1..63.

EXAMPLE

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.

PROG

(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

CROSSREFS

Cf. A088045.

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Sep 20 2003

EXTENSIONS

More terms from David Wasserman, Jun 21 2005

STATUS

approved

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