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

1,1

Links

Ray Chandler, Table of n, a(n) for n = 1..64

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

Cf. A001065, A249108, A249396, A249397.

Sequence in context: A062238 A146249 A248834 * A342221 A074974 A191913

Adjacent sequences: A249106 A249107 A249108 * A249110 A249111 A249112

Keyword

nonn

Author

Paolo P. Lava, Oct 21 2014

Extensions

a(22)-a(38) from Michel Marcus, Nov 09 2014

Status

approved