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

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

Offset

0,1

Links

Table of n, a(n) for n=0..24.

Example

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

Maple

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

Mathematica

a[n_] := Module[{j, pj, pn = PartitionsP[n]}, For[j = n+1, True, j++, If[Divisible[pj = PartitionsP[j], pn], Return[pj]]]];
Table[a[n], {n, 1, 25}] (* Jean-François Alcover, Jul 08 2024 *)

Prog

(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))

Crossrefs

Cf. A000041.

Sequence in context: A082811 A014353 A353101 * A190632 A036110 A143807

Adjacent sequences: A079029 A079030 A079031 * A079033 A079034 A079035

Keyword

nonn

Author

Benoit Cloitre, Feb 01 2003

Extensions

More terms from Emeric Deutsch, May 16 2006

a(0) prepended by Alois P. Heinz, Jul 08 2024

Status

approved