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 A227977 Numbers n for which n = sigma*(x) = sigma*(y), where n = x + y and sigma*(n) is the sum of the anti-divisors of n. 0
 154, 3136, 5536, 20066, 136036, 9550080, 78011830 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Up to a(7) the triples (n, x, y) are (154, 77, 77), (3136, 1568, 1568)(5536, 2768, 2768), (20066, 10368, 9698), (136036, 80753, 55283), (9550080, 4775040, 4775040), (78011830, 39348342, 38663488). - Giovanni Resta, Oct 08 2013 LINKS EXAMPLE n = 20066 = 9698 + 10368. Anti-divisors of 9698 are 3, 4, 5, 7, 9, 15, 17, 45, 52, 119, 163, 431, 1141, 1293, 1492, 2155, 2771, 3879, 6465 and their sum is 20066 that is equal to n. Anti-divisors of 10368 are 5, 11, 13, 29, 55, 65, 89, 143, 145, 233, 256, 319, 377, 715, 768, 1595, 1885, 2304, 4147, 6912 and their sum is 20066 that is equal to n. MAPLE with(numtheory); P:=proc(q) local a, b, i, j, k, n; for n from 1 to q do for i from 1 to trunc(n/2) do k:=0; j:=i; while j mod 2<>1 do k:=k+1; j:=j/2; od; a:=sigma(2*i+1)+sigma(2*i-1)+sigma(i/2^k)*2^(k+1)-6*i-2; k:=0; j:=n-i; while j mod 2<>1 do k:=k+1; j:=j/2; od; b:=sigma(2*(n-i)+1)+sigma(2*(n-i)-1)+sigma((n-i)/2^k)*2^(k+1)-6*(n-i)-2; if a=b and a=n then print(n); fi; od; od; end: P(10^6); CROSSREFS Cf. A066272, A066417, A210732. Sequence in context: A160853 A235099 A332421 * A282557 A200709 A248657 Adjacent sequences:  A227974 A227975 A227976 * A227978 A227979 A227980 KEYWORD nonn AUTHOR Paolo P. Lava, Oct 07 2013 EXTENSIONS a(5)-a(7) from Giovanni Resta, Oct 08 2013 STATUS approved

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Last modified October 24 20:35 EDT 2021. Contains 348233 sequences. (Running on oeis4.)