

A229953


Numbers k for which k = sigma(sigma(x)) = sigma(sigma(y)) for some x and y such that k = x + y.


0



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

1,1


COMMENTS

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


LINKS



EXAMPLE

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)).


MAPLE

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(nj)) and sigma(sigma(j))=n then print(n);
fi; od; od; end: P(10^6);


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



