

A307857


Number of partitions of n into 1, 2 or 3 nonprime parts.


0



1, 1, 1, 1, 1, 2, 1, 3, 3, 4, 3, 5, 4, 6, 5, 9, 7, 10, 8, 12, 10, 15, 11, 18, 15, 20, 17, 24, 19, 28, 22, 30, 26, 36, 29, 41, 34, 42, 37, 51, 41, 55, 47, 59, 53, 66, 54, 73, 63, 78, 70, 85, 72, 94, 81, 99, 89, 108, 92, 118, 102, 121, 110, 135, 117, 143, 126
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OFFSET

1,6


LINKS

Table of n, a(n) for n=1..67.
Index entries for sequences related to partitions


FORMULA

a(n) = A005171(n) + ( Sum_{i=1..floor(n/2)} A005171(i) * A005171(ni) ) + ( Sum_{j=1..floor(n/3)} Sum_{i=j..floor(nj)/2)} A005171(i) * A005171(j) * A005171(nij) ).


EXAMPLE

a(9) = 3, because 9 can be written as the sum of nonprimes with at most 3 parts in three ways: 9 = 8+1 = 4+4+1.
a(10) = 4, because 10 can be written as the sum of nonprimes with at most 3 parts in four ways: 10 = 9+1 = 6+4 = 8+1+1.
a(11) = 3, because 11 can be written as the sum of nonprimes with at most 3 parts in three ways: 10+1 = 9+1+1 = 6+4+1.
a(12) = 5, because 12 can be written as the sum of nonprimes with at most 3 parts in five ways: 12 = 8+4 = 6+6 = 10+1+1 = 4+4+4.


CROSSREFS

Cf. A005171, A018252, A071335.
Sequence in context: A048619 A116087 A163281 * A116921 A173989 A093068
Adjacent sequences: A307854 A307855 A307856 * A307858 A307859 A307860


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, May 01 2019


STATUS

approved



