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A229953
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Numbers k for which k = sigma(sigma(x)) = sigma(sigma(y)) for some x and y such that k = x + y.
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0
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4, 8, 32, 60, 128, 8192, 43200, 69360, 120960, 131072, 524288, 4146912, 6549984, 12927600, 13335840, 16329600, 34715520, 51603840, 57879360, 59633280, 107775360, 160797000, 169155840, 252067200, 371226240, 391789440, 436230144, 439883136, 489888000, 657296640
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OFFSET
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1,1
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COMMENTS
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A072868 is a subsequence of this sequence. Any term x of A072868 can be expressed as x = 2*sigma(sigma(x/2)).
Note the analogy with amicable pair sums (A180164) which satisfy a similar condition: k = sigma(x) = sigma(y) where k = x + y. - Michel Marcus, Oct 07 2013
When terms do not belong to A072868, then they belong to A159886, and the (x,y) couples are (23,37), (14999,28201), (34673,34687), (55373,65587), (2056961,2089951), (2458187,4091797), (4586987,8340613), (5174363,8161477), (6204767,10124833), (15788453,18927067), (25748273,25855567), (20699927,37179433), (22239647,37393633), ... - Michel Marcus, Oct 08 2013
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LINKS
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EXAMPLE
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4 = 2 + 2 = 2*sigma(sigma(2)).
8 = 4 + 4 = 2*sigma(sigma(4)).
32 = 16 + 16 = 2*sigma(sigma(16)).
60 = 23 + 37 = sigma(sigma(23)) = sigma(sigma(37)).
128 = 64 + 64 = 2*sigma(sigma(64)).
8192 = 4096 + 4096 = 2*sigma(sigma(4096)).
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MAPLE
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with(numtheory); P:=proc(q) local j, n;
for n from 1 to q do for j from 1 to trunc(n/2) do
if sigma(sigma(j))=sigma(sigma(n-j)) and sigma(sigma(j))=n then print(n);
fi; od; od; end: P(10^6);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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