A249108 Composite numbers whose sum of aliquot parts divides the sum of aliquot parts of the numbers less than or equal to n and relatively prime to n.

133, 667, 961, 1007, 2013, 3986, 5662, 15979, 17453, 33233, 46943, 51101, 94870, 101444, 119045, 134298, 136957, 179567, 188897, 213511, 226203, 246149, 279749, 299139, 306667, 310157, 434531, 449087, 449183, 518459, 519203

Offset: 1

Author

Paolo P. Lava, Oct 21 2014

Keywords

• nonn

Examples

			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.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..40

Crossrefs

Cf. A001065, A249109, A249396, A249397.

Programs

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);

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

Extensions

a(10)-a(13) from Michel Marcus, Nov 07 2014

a(14)-a(31) from Ray Chandler, Nov 12 2014