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

1,1

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

Cf. A001065, A249109, A249396, A249397.

Sequence in context: A267288 A334037 A137879 * A020237 A217690 A117565

Adjacent sequences: A249105 A249106 A249107 * A249109 A249110 A249111

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