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 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. 2
 1, 8, 50, 128, 228, 9976, 32768, 41890, 47668, 53064, 501888, 564736, 1207944, 12026888, 14697568, 29720448, 2147483648, 2256502784, 21471264576, 35929849856 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 17 03:50 EDT 2024. Contains 373432 sequences. (Running on oeis4.)