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

12, 56, 672, 992, 11904, 16256, 55552, 195072, 666624, 910336, 10924032, 16125952, 67100672, 193511424, 805208064, 903053312, 3757637632, 10836639744, 17179738112, 45091651584, 66563866624, 206156857344, 274877382656, 798766399488, 962065334272, 1090788524032

Offset: 1

Author

Antonio Roldán, May 19 2013

Keywords

• nonn

Comments

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).

This sequence is supersequence of A139256.

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).

Examples

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

Crossrefs

Cf. A225882, A225881.

Programs

PARI

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