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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).
1
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
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
Sequence in context: A006737 A128869 A186669 * A256238 A359714 A370938
KEYWORD
nonn
AUTHOR
Paolo P. Lava, May 21 2015
STATUS
approved