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Nonprime-power sigma-perfect numbers: numbers n such that NPPSigma(n)=2*n, where, 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}.
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%I #4 Apr 19 2016 01:07:34

%S 6,4560,13770,111552,256011840

%N Nonprime-power sigma-perfect numbers: numbers n such that NPPSigma(n)=2*n, where, 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 NPPSigma(2^5*7^4)=(1+2+2^4)*(1+7+7^4)=45771

%e 13770=2*3^4*5*17 so NPPSigma(2*3^4*5*17)=(1+2^1)*(1+3^1+3^4)*(1+5^1)*(1+17^1)=2*13770.

%e Factorizations : 2*3, 2^4*3*5*19, 13770=2*3^4*5*17, 2^6*3*7*83, ...

%Y Cf. A096290.

%K nonn

%O 1,1

%A _Yasutoshi Kohmoto_, Nov 06, 2004

%E Corrected and extended by _Farideh Firoozbakht_, Nov 07 2004