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A225880 Numbers that can be expressed as the product of largest odd proper divisor and the sum of odd proper divisors. 2

%I

%S 12,56,672,992,11904,16256,55552,195072,666624,910336,10924032,

%T 16125952,67100672,193511424,805208064,903053312,3757637632,

%U 10836639744,17179738112,45091651584,66563866624,206156857344,274877382656,798766399488,962065334272,1090788524032

%N Numbers that can be expressed as the product of largest odd proper divisor and the sum of odd proper divisors.

%C The numbers a(n) can be expressed as 2^(m+n+p+...)*(2^m-1)*(2^n-1)*(2^p-1)... with 2^m-1, 2^n-1, 2^p-1 distinct Mersenne primes (A000668(n)). Example: 55552 = 2^6*7*31=2^6*(2^3-1)*(2^5-1).

%C This sequence is supersequence of A139256.

%C The number a(n) is in A139256 or a(n) is product of twice even perfect numbers A139256(n). Example: 1090788524032 = 16256*67100672 = (2*8128)*(2*33550336) = A139256(4) * A139256(5).

%e 11904 = 93*(93+31+3+1).

%o (PARI)

%o gdivodd(n)={m=n;while(m/2==m\2,m=m/2);return(m)}

%o {for (n=2,2*10^8,m=gdivodd(n)*sumdiv(n, d, d*(d%2));if(m==n,print(n)))}

%Y Cf. A225882, A225881.

%K nonn

%O 1,1

%A _Antonio Roldán_, May 19 2013

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Last modified October 22 09:56 EDT 2019. Contains 328315 sequences. (Running on oeis4.)