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%I #9 Oct 03 2015 23:26:46
%S 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,
%T 172,174,227,232,298,303,389,396,498,513,639,655,814,834,1025,1057,
%U 1287,1326,1610,1657,1995,2063,2469,2548,3039,3138,3720,3851,4539,4696,5523
%N Number of distinct values of Product_{p is a part of P} (p-1) when P ranges over all partitions of n.
%H Max Alekseyev, <a href="/A139807/a139807.txt">Proof of the conjecture</a>
%F 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_
%p 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
%Y Cf. A034891.
%K nonn
%O 1,2
%A _Vladeta Jovovic_, May 23 2008
%E More terms from _R. J. Mathar_, May 29 2008
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