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
Keywords
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
Programs
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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);
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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