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

1,7

Comments

a(p) = A023894(p) - 1 for p prime.

Links

Table of n, a(n) for n=1..62.

Example

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).

Crossrefs

Cf. A079413, A023894, A051613, A000961.

Sequence in context: A146431 A212183 A115716 * A356655 A306861 A262940

Adjacent sequences: A079409 A079410 A079411 * A079413 A079414 A079415

Keyword

nonn

Author

Reinhard Zumkeller, Jan 07 2003

Status

approved