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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.
2
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
1,1
LINKS
EXAMPLE
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.
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);
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Oct 21 2014
EXTENSIONS
a(22)-a(38) from Michel Marcus, Nov 09 2014
STATUS
approved