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 A236758 Number of partitions of 3n into 3 parts with smallest part prime. 5
 0, 1, 3, 6, 10, 14, 20, 25, 32, 37, 45, 51, 61, 68, 79, 86, 98, 106, 120, 129, 144, 153, 169, 179, 196, 206, 223, 233, 251, 262, 282, 294, 315, 327, 348, 360, 382, 395, 418, 431, 455, 469, 495, 510, 537, 552, 580, 596, 625, 641, 670, 686, 716, 733, 764, 781 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS FORMULA a(n) = Sum_{i=1..n} A010051(i) * (2n - 2i + 1 - floor((n - i + 1)/2). EXAMPLE Count the primes in last column for a(n): 13 + 1 + 1 12 + 2 + 1 11 + 3 + 1 10 + 4 + 1 9 + 5 + 1 8 + 6 + 1 7 + 7 + 1 10 + 1 + 1 11 + 2 + 2 9 + 2 + 1 10 + 3 + 2 8 + 3 + 1 9 + 4 + 2 7 + 4 + 1 8 + 5 + 2 6 + 5 + 1 7 + 6 + 2 7 + 1 + 1 8 + 2 + 2 9 + 3 + 3 6 + 2 + 1 7 + 3 + 2 8 + 4 + 3 5 + 3 + 1 6 + 4 + 2 7 + 5 + 3 4 + 4 + 1 5 + 5 + 2 6 + 6 + 3 4 + 1 + 1 5 + 2 + 2 6 + 3 + 3 7 + 4 + 4 3 + 2 + 1 4 + 3 + 2 5 + 4 + 3 6 + 5 + 4 1 + 1 + 1 2 + 2 + 2 3 + 3 + 3 4 + 4 + 4 5 + 5 + 5 3(1) 3(2) 3(3) 3(4) 3(5) .. 3n --------------------------------------------------------------------- 0 1 3 6 10 .. a(n) MAPLE with(numtheory); A236758:=n->sum((pi(n) - pi(n-1)) * (2*n - 2*i + 1 - floor((n - i + 1)/2)), i=1..n); seq(A236758(n), n=1..100); MATHEMATICA Table[Sum[(PrimePi[i] - PrimePi[i - 1]) (2 n - 2 i + 1 - Floor[(n - i + 1)/2]), {i, n}], {n, 100}] PROG (Sage) def a(n): return sum(1 for L in Partitions(3*n, length=3).list() if is_prime(L[2])) CROSSREFS Cf. A019298, A235988, A236364, A236762, A010051 (for function isprime). Sequence in context: A330257 A079552 A334454 * A272058 A244360 A183863 Adjacent sequences: A236755 A236756 A236757 * A236759 A236760 A236761 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Jan 30 2014 STATUS approved

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Last modified February 6 23:12 EST 2023. Contains 360111 sequences. (Running on oeis4.)