A099723 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}.

6, 4560, 13770, 111552, 256011840

Offset

1,1

Links

Table of n, a(n) for n=1..5.

Example

NPPSigma(2^5*7^4)=(1+2+2^4)*(1+7+7^4)=45771
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.
Factorizations : 2*3, 2^4*3*5*19, 13770=2*3^4*5*17, 2^6*3*7*83, ...

Crossrefs

Cf. A096290.

Sequence in context: A317485 A209310 A268504 * A226499 A343096 A066061

Adjacent sequences: A099720 A099721 A099722 * A099724 A099725 A099726

Keyword

nonn

Author

Yasutoshi Kohmoto, Nov 06, 2004

Extensions

Corrected and extended by Farideh Firoozbakht, Nov 07 2004

Status

approved