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 A341977 Number of partitions of n into 6 distinct primes (counting 1 as a prime). 10
 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 1, 5, 0, 4, 1, 5, 2, 8, 1, 7, 2, 8, 4, 12, 2, 12, 6, 14, 7, 17, 5, 18, 8, 20, 11, 26, 10, 27, 15, 30, 18, 36, 17, 36, 22, 41, 28, 48, 25, 49, 35, 56, 40, 61, 38, 64, 50, 73, 56, 77, 54, 82, 70, 93, 74, 96, 78, 106, 92, 114, 100 (list; graph; refs; listen; history; text; internal format)
 OFFSET 29,7 LINKS Alois P. Heinz, Table of n, a(n) for n = 29..10000 MAPLE b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<0, 0, (p-> `if`(p>n, 0, x*b(n-p, i-1)))( `if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 7) end: a:= n-> coeff(b(n, numtheory[pi](n)), x, 6): seq(a(n), n=29..100); # Alois P. Heinz, Feb 24 2021 MATHEMATICA m = 6; b[n_, i_] := b[n, i] = Series[If[n == 0, 1, If[i < 0, 0, Function[p, If[p > n, 0, x*b[n - p, i - 1]]][ If[i == 0, 1, Prime[i]]] + b[n, i - 1]]], {x, 0, m + 1}]; a[n_] := Coefficient[b[n, PrimePi[n]], x, m]; Table[a[n], {n, 29, 100}] (* Jean-François Alcover, Mar 06 2021, after Alois P. Heinz *) CROSSREFS Cf. A008578, A036497, A219200, A341949, A341973, A341974, A341975, A341976. Sequence in context: A025815 A219199 A029225 * A309937 A116127 A039979 Adjacent sequences: A341974 A341975 A341976 * A341978 A341979 A341980 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Feb 24 2021 STATUS approved

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Last modified September 17 17:26 EDT 2024. Contains 375990 sequences. (Running on oeis4.)