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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 (list; graph; refs; listen; history; text; internal format)
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
Graeme L. Cohen and Herman J. J. te Riele, Iterating the sum-of-divisors function, Experiment. Math. (1996) vol. 5, no. 2, pp. 91-100 (see merge at n=60 in tree of section 4 page 97).
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(n-j)) and sigma(sigma(j))=n then print(n);
fi; od; od; end: P(10^6);
CROSSREFS
Sequence in context: A173617 A034041 A050442 * A331408 A291938 A358046
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Oct 04 2013
EXTENSIONS
a(7)-a(20) from Giovanni Resta, Oct 06 2013
a(21)-a(30) from Donovan Johnson, Oct 08 2013
STATUS
approved

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Last modified July 15 10:40 EDT 2024. Contains 374332 sequences. (Running on oeis4.)