

A139807


Number of distinct values of Product_{p is a part of P} (p1) when P ranges over all partitions of n.


1



1, 2, 2, 3, 3, 5, 4, 8, 7, 11, 11, 17, 16, 25, 24, 35, 35, 50, 49, 70, 69, 94, 96, 129, 129, 172, 174, 227, 232, 298, 303, 389, 396, 498, 513, 639, 655, 814, 834, 1025, 1057, 1287, 1326, 1610, 1657, 1995, 2063, 2469, 2548, 3039, 3138, 3720, 3851, 4539, 4696, 5523
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


LINKS



FORMULA

Conjecture: G.f. is x/(1x)+((1x^12)/((1x^2)*(1x^5)))*(1/Product_{k>0} (1x^(prime(k)+1))), i.e. a(n) = 1 + number of partitions of n into parts of the form p+1, p a prime, excluding 12 and including 2 and 5. Added May 28 2008: The conjecture is correct! See the link.  Max Alekseyev


MAPLE

A139807 := proc(n) local g, i, p ; g := (1x^12)/(1x^2)/(1x^5) ; for i from 1 do p := ithprime(i) ; if p > n then break ; fi ; g := taylor(g/(1x^(p+1)), x=0, n+1) ; od: coeftayl( g+1/(1x), x=0, n) ; end: seq(A139807(n), n=1..80) ; # R. J. Mathar, May 29 2008


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



