A238765 Numbers k such that if x = Sum_{j|k, j<k} (sigma(j) - j) then k = Sum_{j|x, j<k} (sigma(j) - j).

198, 608, 11322, 15450, 17874, 20826, 33894, 41022, 56608, 1259910, 1764414, 3055150, 565344850, 579667086, 907521650

Offset

1,1

Comments

A066218 is a subsequence. It lists the fixed points of the transform n -> Sum_{j|n, j<n} (sigma(j)- j).

Links

Table of n, a(n) for n=1..15.

Example

Aliquot divisors of 15450 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 103, 150, 206, 309, 515, 618, 1030, 1545, 2575, 3090, 5150, 7725. Their respective sigma(k)-k are 0, 1, 1, 1, 6, 8, 9, 6, 42, 43, 49, 1, 222, 106, 107, 109, 630, 842, 951, 649, 4398, 4522, 5171 and their sum is equal to 17874.
Aliquot divisors of 17874 are 1, 2, 3, 6, 9, 18, 27, 54, 331, 662, 993, 1986, 2979, 5958, 8937. Their respective sigma(k)-k are 0, 1, 1, 6, 4, 21, 13, 66, 1, 334, 335, 1998, 1337, 6990, 4343 and their sum is equal to 15450.

Maple

with(numtheory); P:=proc(q) local a, b, c, i, n;
for n from 1 to q do a:=sort([op(divisors(n))]); b:=0;
for i from 1 to nops(a)-1 do b:=b+sigma(a[i])-a[i]; od;
a:=sort([op(divisors(b))]); c:=0;
for i from 1 to nops(a)-1 do c:=c+sigma(a[i])-a[i]; od;
if n=c then print(n); fi; od; end: P(10^6);

Crossrefs

Cf. A000203, A066218.

Sequence in context: A083264 A202526 A221219 * A066218 A304614 A357076

Adjacent sequences: A238762 A238763 A238764 * A238766 A238767 A238768

Keyword

nonn,more,hard

Author

Paolo P. Lava, Mar 05 2014

Extensions

a(13)-a(15) from Michel Marcus, Mar 07 2014

Status

approved