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%I #10 Feb 28 2020 22:51:52
%S 30,22,490,42,1575,10143,4565,37338,1121505,792,12310,124754,5392783,
%T 1575,31185,386155,23338469,75175,1121505,92669720,5604,173525,
%U 3087735,342325709,1002,10143,386155,8118264,1188908248,571701605655
%N 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.
%D Robert Kanigel, The Man Who Knew Infinity, Washington Square Press, New York, 1991, page 302.
%e The row n=2 contains A000041(9)=30 from m=2, prime(m)=3.
%e The row n=3 contains A000041(8)=22 from m=1, prime(m)=2, and A000041(19)=490 from m=3, prime(m)=5.
%e The triangle starts in row n=2 as:
%e 30;
%e 22, 490;
%e 42, 1575, 10143;
%e 4565, 37338, 1121505;
%e 792, 12310, 124754, 5392783;
%e 1575, 31185, 386155, 23338469;
%e 75175, 1121505, 92669720;
%e 5604, 173525, 3087735, 342325709;
%e 1002, 10143, 386155, 8118264, 1188908248, 571701605655;
%t 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]
%Y Cf. A000041, A117750.
%K nonn,tabf
%O 2,1
%A _Roger L. Bagula_, Apr 14 2006
%E Comments and definition rephrased, offset corrected - the Assoc. Eds. of the OEIS, Jun 27 2010
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