A079412 Number of ways to write n as sum of prime powers p^e such that e>0 and p does not divide n.
0, 0, 0, 0, 1, 0, 3, 1, 3, 1, 11, 1, 18, 3, 7, 5, 43, 2, 65, 5, 24, 10, 137, 4, 115, 17, 84, 16, 379, 3, 519, 42, 152, 47, 317, 12, 1267, 73, 334, 41, 2213, 9, 2897, 107, 344, 174, 4871, 32, 3733, 100, 1369, 245, 10218, 51, 4037, 235, 2607, 554, 20586, 23, 25792, 795
Offset: 1
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Examples
13 = 11+2 = 3^2+2^2 = 3^2+2+2 = 2^3+5 = 2^3+3+2 = 7+2^2+2 = 7+3+3 = 7+2+2+2 = 5+5+3 = 5+2^2+2^2 = 5+2^2+2+2 = 5+3+3+2 = 5+2+2+2+2 = 2^2+2^2+3+2 = 2^2+3+3+3 = 2^2+3+2+2+2 = 3+3+3+2+2 = 3+2+2+2+2+2, therefore a(13)=18, (A023894(13)=19, A079413(13)=3); 14 = 11+3 = 3^2+5 = 5+3+3+3, therefore a(14)=3, (A023894(14)=23, A079413(14)=2).
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