OFFSET
1,1
LINKS
Ray Chandler, Table of n, a(n) for n = 1..40
EXAMPLE
Numbers coprime to 133 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 90, 92, 93, 94, 96, 97, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 113, 115, 116, 117, 118, 120, 121, 122, 123, 124, 125, 127, 128, 129, 130, 131, 132. The sum of their aliquot parts is 4401; sigma(133) - 133 = 27 and 4401 / 27 = 163.
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, s = 0; for (i=1, n, if (gcd(n, i) == 1, s += sigma(i)-i); ); if ((s % (sigma(n)-n)) == 0, print1(n, ", ")); ); } \\ Michel Marcus, Nov 07 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Oct 21 2014
EXTENSIONS
a(10)-a(13) from Michel Marcus, Nov 07 2014
a(14)-a(31) from Ray Chandler, Nov 12 2014
STATUS
approved