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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
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 (list; graph; refs; listen; history; text; internal format)
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: A081756 A027147 A095724 * A224832 A139256 A166997

Adjacent sequences:  A225877 A225878 A225879 * A225881 A225882 A225883

KEYWORD

nonn

AUTHOR

Antonio Roldán, May 19 2013

STATUS

approved

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Last modified July 25 04:48 EDT 2017. Contains 289779 sequences.