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A079032
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Smallest nontrivial partition number divisible by the n-th partition number.
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0
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2, 2, 22, 15, 15, 42, 22, 30, 176, 133230930, 2436, 8118264, 231, 413766180933342362, 31185, 118114304, 31185, 31185, 31185, 670448123060170, 426088638015652413417, 1973678121921532286407950000, 133230930, 101121613386982294887579670, 213636919820625
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OFFSET
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0,1
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LINKS
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EXAMPLE
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a(5)=42 because the 5th partition number is 7 and the next partition number divisible by 7 is 42.
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MAPLE
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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
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MATHEMATICA
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a[n_] := Module[{j, pj, pn = PartitionsP[n]}, For[j = n+1, True, j++, If[Divisible[pj = PartitionsP[j], pn], Return[pj]]]];
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PROG
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(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))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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