A258135 Let s denote the sum of the abundant numbers in the aliquot parts of x. Sequence lists numbers x such that sigma(s) = usigma(x), where usigma(x) is the sum of the unitary divisors of x (A034448).

760, 918, 924, 1540, 4648, 6204, 8260, 15210, 20070, 21450, 27450, 30114, 41052, 47344, 50464, 55952, 60040, 60534, 61088, 63080, 77024, 77994, 81320, 99084, 117572, 132210, 136068, 150750, 169480, 215325, 215740, 226422, 309160, 476196, 495444, 505720, 530292

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Example

Aliquot parts of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380. Abundant numbers are 20, 40 and 380. Then sigma(20+40+380) = sigma(440) = 1080 = usigma(760).
Aliquot parts of 918 are 1, 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 102, 153, 306, 459. Abundant numbers are 18, 54, 102 and 306. Then sigma(18+54+102+306) = sigma(480) = 1512 = usigma(918).
Aliquot parts of 924 are 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462. Abundant numbers are 12, 42, 66, 84, 132, 308 and 462. Then sigma(12+42+66+84+132+308+462) = sigma(1106) = 1920 = usigma(924).

Maple

with(numtheory); P:=proc(q) local a, b, d, k, n; for n from 1 to q do
a:=sort([op(divisors(n))]); b:=0; d:=0;
for k from 1 to nops(a)-1 do if sigma(a[k])>2*a[k] then b:=b+a[k]; fi; od;
for k from 1 to nops(a) do if gcd(a[k], n/a[k])=1 then d:=d+a[k]; fi; od;
if sigma(b)=d then print(n); fi; od; end: P(10^9);

Crossrefs

Cf. A000203, A005101, A034448, A258135.

Sequence in context: A034414 A157983 A014747 * A247400 A234892 A233879

Adjacent sequences: A258132 A258133 A258134 * A258136 A258137 A258138

Keyword

nonn

Author

Paolo P. Lava, May 21 2015

Status

approved