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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
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
Sequence in context: A299049 A299811 A280600 * A258635 A300494 A300933
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.)