

A229953


Numbers n for which n = sigma(sigma(x)) = sigma(sigma(y)), where n = 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 subset 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: n = sigma(x) = sigma(y) where n = 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

Table of n, a(n) for n=1..30.
Graeme L. Cohen and Herman J. J. te Riele, Iterating the sumofdivisors function, Experiment. Math. (1996) vol. 5, no. 2, pp. 91100 (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(nj)) and sigma(sigma(j))=n then print(n);
fi; od; od; end: P(10^6);


CROSSREFS

Cf. A000203, A072868.
Sequence in context: A173617 A034041 A050442 * A331408 A291938 A094015
Adjacent sequences: A229950 A229951 A229952 * A229954 A229955 A229956


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



