A250399 Composite numbers whose sum of aliquot parts divides the sum of their unrelated numbers.
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
Keywords
Examples
There is no unrelated number to 4. Therefore 0 / (sigma(4)-4) = 0 / (7-4) = 0 is an 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 an integer.
Programs
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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);
Comments