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A250399
Composite numbers whose sum of aliquot parts divides the sum of their unrelated numbers.
1
4, 14, 63, 85, 1649, 3127, 6401, 11521, 14121, 30005, 30629, 33101, 45671, 58829, 78227, 82947, 90581, 110975, 159877, 185399, 227341, 308179, 331918, 336299, 359413, 439619, 466759, 476677, 494321, 618701, 666409, 898967, 1044611, 1113641, 1228417, 1248707
OFFSET
1,1
COMMENTS
For a definition of unrelated number see A045763.
EXAMPLE
There is no unrelated number to 4. Therefore 0 / (sigma(4)-4) = 0 / (7-4) = 0 is integer.
Unrelated numbers to 14 are 4, 6, 8, 10, 12 and their sum is 40. Now, 40 / (sigma(14) - 14) = 40 / (24 - 14) = 40 / 10 = 4, that is integer.
MAPLE
with(numtheory); P:=proc(q) local n;
for n from 1 to q do if not isprime(n) then
if type((1+n*(n+1)/2-sigma(n)-n*phi(n)/2)/(sigma(n)-n), integer)
then print(n); fi; fi; od; end: P(10^5);
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Nov 21 2014
STATUS
approved