A117749 Irregular triangle which contains in row n those partition numbers A000041(n*prime(m) + m + 1) which are congruent to 0 mod prime(m) for 1 <= m <= n.

30, 22, 490, 42, 1575, 10143, 4565, 37338, 1121505, 792, 12310, 124754, 5392783, 1575, 31185, 386155, 23338469, 75175, 1121505, 92669720, 5604, 173525, 3087735, 342325709, 1002, 10143, 386155, 8118264, 1188908248, 571701605655

Offset

2,1

References

Robert Kanigel, The Man Who Knew Infinity, Washington Square Press, New York, 1991, page 302.

Links

Table of n, a(n) for n=2..31.

Example

The row n=2 contains A000041(9)=30 from m=2, prime(m)=3.
The row n=3 contains A000041(8)=22 from m=1, prime(m)=2, and A000041(19)=490 from m=3, prime(m)=5.
The triangle starts in row n=2 as:
30;
22, 490;
42, 1575, 10143;
4565, 37338, 1121505;
792, 12310, 124754, 5392783;
1575, 31185, 386155, 23338469;
75175, 1121505, 92669720;
5604, 173525, 3087735, 342325709;
1002, 10143, 386155, 8118264, 1188908248, 571701605655;

Mathematica

b = Table[Flatten[Table[If[Mod[PartitionsP[Prime[n]*m + n + 1], Prime[n]] == \ 0, PartitionsP[Prime[n]*m + n + 1], {}], {n, 1, m}]], {m, 1, 10}] Flatten[b]

Crossrefs

Cf. A000041, A117750.

Sequence in context: A040872 A361029 A268855 * A283621 A100935 A112026

Adjacent sequences: A117746 A117747 A117748 * A117750 A117751 A117752

Keyword

nonn,tabf

Author

Roger L. Bagula, Apr 14 2006

Extensions

Comments and definition rephrased, offset corrected - the Assoc. Eds. of the OEIS, Jun 27 2010

Status

approved