A249109 Composite numbers whose sum of aliquot parts divides the sum of the aliquot parts of the numbers less than or equal to n and not relatively prime to n.
15, 26, 27, 38, 76, 194, 531, 1445, 1501, 2923, 2988, 4427, 4499, 4769, 5817, 7831, 9523, 10602, 12412, 14963, 16117, 24863, 26768, 29041, 29329, 30229, 36577, 45246, 49817, 58483, 58823, 71165, 75469, 76273, 79799, 83429, 86941, 94037
Offset: 1
Keywords
Examples
Numbers not coprime to 15 are 3, 5, 6, 9, 10, 12, 15. Then, sigma(3) - 3 = 1, sigma(5) - 5 = 1, sigma(6) - 6 = 6, sigma(9) - 9 = 4, sigma(10) - 10 = 8, sigma(12) - 12 = 16, sigma(15) - 15 = 9; their sum is 1 + 1 + 6 + 4 + 8 + 16 + 9 = 45 and 45 / 9 = 5.
Links
- Ray Chandler, Table of n, a(n) for n = 1..64
Programs
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Maple
with(numtheory): P:=proc(q) local a,k,n; for n from 2 to q do if not isprime(n) then a:=0; for k from 1 to n do if gcd(k,n)>1 then a:=a+sigma(k)-k; fi; od; if type(a/(sigma(n)-n),integer) then print(n); fi; fi; od; end: P(10^9);
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PARI
lista(nn) = {forcomposite(n=1, nn, if (sum(k=1, n, if (gcd(k,n) !=1, sigma(k)-k)) % (sigma(n) - n) == 0, print1(n, ", ")););} \\ Michel Marcus, Nov 09 2014
Extensions
a(22)-a(38) from Michel Marcus, Nov 09 2014