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URL: https://oeis.org/A341462

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A341462
Number of partitions of n into 4 distinct nonprime parts.
10
1, 1, 1, 1, 2, 2, 3, 3, 5, 5, 7, 6, 10, 9, 13, 12, 17, 17, 21, 21, 28, 28, 34, 33, 42, 43, 51, 53, 61, 63, 73, 76, 87, 91, 102, 104, 119, 123, 137, 143, 157, 164, 179, 187, 205, 215, 232, 239, 262, 272, 294, 309, 327, 341, 365, 381, 406, 427, 448, 465
OFFSET
19,5
MAPLE
b:= proc(n, i, t) option remember; `if`(n=0,
`if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
`if`(isprime(i), 0, b(n-i, min(n-i, i-1), t-1))))
end:
a:= n-> b(n$2, 4):
seq(a(n), n=19..78); # Alois P. Heinz, Feb 12 2021
MATHEMATICA
b[n_, i_, t_] := b[n, i, t] = If[n == 0,
If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
If[PrimeQ[i], 0, b[n - i, Min[n - i, i - 1], t - 1]]]];
a[n_] := b[n, n, 4];
Table[a[n], {n, 19, 78}] (* Jean-François Alcover, Jul 13 2021, after Alois P. Heinz *)
Table[Length[Select[IntegerPartitions[n, {4}], Length[#]==Length[ Union[ #]] && NoneTrue[#, PrimeQ]&]], {n, 19, 80}] (* Harvey P. Dale, Nov 07 2021 *)
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 12 2021
STATUS
approved