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A139807 Number of distinct values of Product_{p is a part of P} (p-1) 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

Table of n, a(n) for n=1..56.

Max Alekseyev, Proof of the conjecture

FORMULA

Conjecture: G.f. is x/(1-x)+((1-x^12)/((1-x^2)*(1-x^5)))*(1/Product_{k>0} (1-x^(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 := (1-x^12)/(1-x^2)/(1-x^5) ; for i from 1 do p := ithprime(i) ; if p > n then break ; fi ; g := taylor(g/(1-x^(p+1)), x=0, n+1) ; od: coeftayl( g+1/(1-x), x=0, n) ; end: seq(A139807(n), n=1..80) ; # R. J. Mathar, May 29 2008

CROSSREFS

Cf. A034891.

Sequence in context: A114328 A275234 A097366 * A308465 A276119 A167755

Adjacent sequences:  A139804 A139805 A139806 * A139808 A139809 A139810

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, May 23 2008

EXTENSIONS

More terms from R. J. Mathar, May 29 2008

STATUS

approved

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Last modified January 21 05:57 EST 2022. Contains 350473 sequences. (Running on oeis4.)