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 A214842 Anti-multiply-perfect numbers. Numbers n for which sigma*(n)/n is an integer, where sigma*(n) is the sum of the anti-divisors of n. 4
 1, 2, 5, 8, 41, 56, 77, 946, 1568, 2768, 5186, 6874, 8104, 17386, 27024, 84026, 167786, 2667584, 4775040, 4921776, 27914146, 505235234, 3238952914, 73600829714, 455879783074, 528080296234, 673223621664, 4054397778846, 4437083907194, 4869434608274, 6904301600914, 7738291969456 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A073930 and A073931 are subsets of this sequence. Like A007691 but using sigma*(n) (A066417) instead of sigma(n) (A000203). Tested up to 167786. Additional terms are 2667584, 4775040, 4921776, 27914146, 505235234, 3238952914, 73600829714 but there may be missing terms among them. LINKS EXAMPLE Anti-divisors of 77 are 2, 3, 5, 9, 14, 17, 22, 31, 51. Their sum is 154 and 154/77=2. MAPLE A214842:= proc(q) local a, k, n; for n from 1 to q do   a:=0; for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then a:=a+k; fi; od;   if type(a/n, integer) then print(n); fi; od; end: A214842(10^10); MATHEMATICA a066417[n_Integer] := Total[Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]]; a214842[n_Integer] := Select[Range[n], IntegerQ[a066417[#]/#] &]; a214842[1200] (* Michael De Vlieger, Aug 08 2014 *) PROG (Python) A214842 = [n for n in range(1, 10**4) if not (sum([d for d in range(2, n, 2) if n%d and not 2*n%d])+sum([d for d in range(3, n, 2) if n%d and 2*n%d in [d-1, 1]])) % n] # Chai Wah Wu, Aug 12 2014 (PARI) sad(n) = vecsum(select(t->n%t && t

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Last modified May 31 00:53 EDT 2020. Contains 334747 sequences. (Running on oeis4.)