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Number of ways to write n as sum of powers p^e of distinct primes p such that e>0 and p does not divide n.
1

%I #3 Mar 30 2012 18:50:30

%S 0,0,0,0,1,0,2,1,2,1,3,1,3,2,3,3,3,2,5,3,4,3,9,3,5,4,6,4,18,3,20,8,7,

%T 8,10,6,30,9,11,8,41,5,47,11,12,13,63,10,42,13,23,16,89,13,35,20,34,

%U 28,126,11,134,35,36,44,57,15,185,40,64,19,236,31,251,64,55,54,117,24,341

%N Number of ways to write n as sum of powers p^e of distinct primes p such that e>0 and p does not divide n.

%C a(p) = A051613(p) - 1 for p prime.

%e 13 = 11+2 = 3^3+2^2 = 2^3+5, therefore a(13)=3, (A051613(13)=4, A054685(13)=6, A079412(13)=18);

%e 14 = 11+3 = 3^2+5, therefore a(14)=2, (A051613(14)=4, A054685(14)=7, A079412(14)=3).

%Y Cf. A079412, A054685, A051613, A023894, A000961.

%K nonn

%O 1,7

%A _Reinhard Zumkeller_, Jan 07 2003