cp's OEIS Frontend

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.

%I A282774 #25 Oct 11 2022 00:53:27
%S A282774 1,8,50,128,228,9976,32768,41890,47668,53064,501888,564736,1207944,
%T A282774 12026888,14697568,29720448,2147483648,2256502784,21471264576,
%U A282774 35929849856
%N 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.
%C A282774 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.
%C A282774 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, ...
%C A282774 a(21) > 6 * 10^10. - _Lucas A. Brown_, Mar 10 2021
%H A282774 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A282774%2B5.py">A282774+5.py</a>
%e A282774 sigma(50) = 93; divisors of 50 are 1, 2, 5, 10, 25, 50 and
%e A282774 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.
%p A282774 with(numtheory): P:=proc(q) local a,b,c,k,n;
%p A282774 for n from 1 to q do if not isprime(n) then a:=sigma(n); b:=sort([op(divisors(n))]);
%p A282774 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);
%o A282774 (PARI) isok(k) = !isprime(k) && !(k % (sigma(k) - sumdiv(k, d, sigma(k) % d))); \\ _Michel Marcus_, Mar 10 2021
%Y A282774 Cf. A000203, A282775.
%K A282774 nonn,more
%O A282774 1,2
%A A282774 _Paolo P. Lava_, Feb 22 2017
%E A282774 a(14)-a(18) from _Giovanni Resta_, Feb 23 2017
%E A282774 Name clarified and a(19)-a(20) from _Lucas A. Brown_, Mar 10 2021