A225880 - OEIS

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

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OFFSET

1,1

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).

LINKS

Table of n, a(n) for n=1..26.

EXAMPLE

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

PROG

(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)))}

CROSSREFS

Cf. A225882, A225881.

Sequence in context: A307741 A027147 A095724 * A224832 A139256 A166997

Adjacent sequences: A225877 A225878 A225879 * A225881 A225882 A225883

KEYWORD

nonn

AUTHOR

Antonio Roldán, May 19 2013

STATUS

approved