A282774 Nonprime numbers k such that sigma(k) - Sum_{j=1..m}{sigma(k) mod d_j} | k, where d_j is one of the m divisors of k.

1, 8, 50, 128, 228, 9976, 32768, 41890, 47668, 53064, 501888, 564736, 1207944, 12026888, 14697568, 29720448, 2147483648, 2256502784, 21471264576, 35929849856

Offset

1,2

Comments

For 1, 228, 501888, 1207944, 29720448, etc., being their ratio equal to 1, we have that Sum_{j=1..m}{sigma(k) mod d_j} is the sum of their aliquot parts.

The ratios for the listed terms are 1, 2, 2, 16, 1, 8, 2048, 2, 2, 22, 1, 512, 1, 25976, 32, 1, 67108864, 32768, ...

a(21) > 6 * 10^10. - Lucas A. Brown, Mar 10 2021

Links

Table of n, a(n) for n=1..20.

Lucas A. Brown, A282774+5.py

Example

sigma(50) = 93; divisors of 50 are 1, 2, 5, 10, 25, 50 and
93 mod 1 + 93 mod 2 + 93 mod 4 + 93 mod 5 + 93 mod 10 + 93 mod 25 + 93 mod 50 = 0 + 1 + 3 + 3 + 18 + 43 = 68 and 50 / (93-68) = 2.

Maple

with(numtheory): P:=proc(q) local a, b, c, k, n;
for n from 1 to q do if not isprime(n) then a:=sigma(n); b:=sort([op(divisors(n))]);
c:=add(a mod b[k], k=1..nops(b)); if type(n/(a-c), integer) then print(n); fi; fi; od; end: P(10^9);

Prog

(PARI) isok(k) = !isprime(k) && !(k % (sigma(k) - sumdiv(k, d, sigma(k) % d))); \\ Michel Marcus, Mar 10 2021

Crossrefs

Cf. A000203, A282775.

Sequence in context: A299049 A299811 A280600 * A258635 A300494 A300933

Adjacent sequences: A282771 A282772 A282773 * A282775 A282776 A282777

Keyword

nonn,more

Author

Paolo P. Lava, Feb 22 2017

Extensions

a(14)-a(18) from Giovanni Resta, Feb 23 2017

Name clarified and a(19)-a(20) from Lucas A. Brown, Mar 10 2021

Status

approved