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 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 14 04:14 EDT 2024. Contains 373393 sequences. (Running on oeis4.)