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A079032 Smallest nontrivial partition number divisible by the n-th partition number. 0

%I

%S 2,22,15,15,42,22,30,176,133230930,2436,8118264,231,

%T 413766180933342362,31185,118114304,31185,31185,31185,670448123060170,

%U 426088638015652413417,1973678121921532286407950000,133230930

%N Smallest nontrivial partition number divisible by the n-th partition number.

%e a(5)=42 because the 5th partition number is 7 and the next partition number divisible by 7 is 42.

%p with(combinat): a:=proc(n) local S,j: S:={}: for j from n+1 to 800 do if type(numbpart(j)/numbpart(n),integer)=true then S:=S union {numbpart(j)} else S:=S fi: od: min(seq(S[i],i=1..nops(S))): end: seq(a(n),n=1..25); # _Emeric Deutsch_, May 16 2006

%o (PARI) a(n)=if(n<0,0,s=n+1; while(polcoeff(1/eta(x),s)%polcoeff(1/eta(x),n)>0,s++); polcoeff(1/eta(x),s))

%Y Cf. A000041.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Feb 01 2003

%E More terms from _Emeric Deutsch_, May 16 2006

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Last modified August 7 22:01 EDT 2022. Contains 355995 sequences. (Running on oeis4.)