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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 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 August 20 23:06 EDT 2018. Contains 313929 sequences. (Running on oeis4.)