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%I #35 Oct 11 2022 00:54:03
%S 1,6,28,120,228,496,672,8128,30240,32760,125640,501888,523776,1207944,
%T 2178540,23569920,29720448,33550336,45532800,142990848,459818240,
%U 1379454720,1476304896,8589869056,14182439040,31998395520,43861478400,51001180160
%N Nonprime numbers k such that k | (sigma(k) - Sum_{j=1..m}{sigma(k) mod d_j}), where d_j is one of the m divisors of k.
%C The multiply-perfect numbers are a subset.
%C For 1, 228, 501888, 1207944, 29720448, etc., their ratio being equal to 1, we have that Sum_{j=1..m}{sigma(k) mod d_j} is the sum of their aliquot parts.
%C The ratios for the listed terms are 1, 2, 2, 3, 1, 2, 3, 2, 4, 4, 2, 1, 3, 1, 4, 4, 1, 2, 4, 4, 3, 4, 3, 2, ...
%C a(29) > 6 * 10^10. - _Lucas A. Brown_, Mar 10 2021
%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A282774%2B5.py">A282774+5.py</a>
%e sigma(228) = 560; divisors of 288 are 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228 and 560 mod 1 + 560 mod 2 + 560 mod 3 + 560 mod 4 + ... + 560 mod 57 + 560 mod 76 + 560 mod 144 + 560 mod 228 = 0 + 0 + 2 + 0 + 2 + 8 + 9 + 28 + 47 + 28 + 104 + 104 = 332 and (560 - 332) / 228 = 1.
%p with(numtheory): P:=proc(q) local a,b,c,k,n;
%p for n from 1 to q do if not isprime(n) then a:=sigma(n); b:=sort([op(divisors(n))]);
%p c:=add(a mod b[k],k=1..nops(b)); if type((a-c)/n,integer) then print(n); fi; fi; od; end: P(10^9);
%o (PARI) isok(k) = if (!isprime(k), my(sk = sigma(k)); (sk - sumdiv(k, d, sk % d)) % k == 0;); \\ _Michel Marcus_, Jun 17 2017
%Y Cf. A000203, A007691, A282774.
%K nonn
%O 1,2
%A _Paolo P. Lava_, Feb 22 2017
%E a(16)-a(24) from _Giovanni Resta_, Feb 23 2017
%E a(25)-a(28) from _Lucas A. Brown_, Mar 10 2021
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