Non prime power sigma
y.kohmoto
zbi74583 at boat.zero.ad.jp
Sat Nov 6 06:59:44 CET 2004
To Neil :
I post a sequence of NPPS perfect number.
%I A000001
%S A000001 6, 4560, 111552
%N A000001 Non Prime Power Sigma perfect number.
NPPSigma(n)=2*n
Here, if n=Product p_i^r_i then
NPPSigma(n)=Product{Sum p_i^s_i, s_i is not a prime number, 0<=s_i<=r_i}
%e A000001 NPPSigma(2^5*7^4)=(1+2+2^4)*(1+7+7^4)=45771
All powers of the terms are not primes.
Factorizations : 2*3, 2^4*3*5*19, 2^6*3*7*83,
%Y A000001 A096290
%K A000001 nonn
%O A000001 1, 1
%A A000001 Yasutoshi Kohmoto (zbi74583 at boat.zero.ad.jp)
I calculated the solutions whose power of factor 2 is up to 16, only
three examples exist.
Isn't it fit to OEIS which needs four terms?
If not, I will describe it on my OEUAI.
Yasutoshi
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