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A225880
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Numbers that can be expressed as the product of largest odd proper divisor and the sum of odd proper divisors.
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2
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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
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1,1
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COMMENTS
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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).
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LINKS
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Table of n, a(n) for n=1..26.
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EXAMPLE
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11904 = 93*(93+31+3+1).
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PROG
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(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)))}
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CROSSREFS
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Cf. A225882, A225881.
Sequence in context: A307741 A027147 A095724 * A224832 A139256 A166997
Adjacent sequences: A225877 A225878 A225879 * A225881 A225882 A225883
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KEYWORD
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nonn
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AUTHOR
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Antonio Roldán, May 19 2013
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STATUS
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approved
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