A258134 Let s denote the sum of the deficient 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).

6, 68, 828, 3444, 6237, 10755, 14595, 15687, 16056, 18837, 27495, 42228, 44408, 46548, 50436, 55750, 68103, 88730, 108560, 129105, 132924, 161490, 168730, 168756, 181935, 189112, 249543, 260540, 273195, 299115, 304425, 313677, 345975, 369472, 424215, 430402

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..1500

Example

Aliquot parts of 6 are 1, 2, 3, which are all deficient numbers. Then sigma(1+2+3) = sigma(6) = 12 = usigma(6).
Aliquot parts of 68 are 1, 2, 4, 17, 34, twhich are all deficient numbers. Then sigma(1+2+4+17+34) = sigma(58) = 90 = usigma(68).
Aliquot parts of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414. Deficient numbers are 1, 2, 3, 4, 9, 23, 46, 69, 92 and 207. Then sigma(1+2+3+4+9+23+46+69+92+207) = sigma(456) = 1200 = usigma(828).

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, A034448.

Sequence in context: A006737 A128869 A186669 * A256238 A359714 A370938

Adjacent sequences: A258131 A258132 A258133 * A258135 A258136 A258137

Keyword

nonn

Author

Paolo P. Lava, May 21 2015

Status

approved