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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.
5
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
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.
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<n, concat(concat(divisors(2*n-1), divisors(2*n+1)), 2*divisors(n)))); \\ A066417
isok(n) = denominator(sad(n)/n) == 1; \\ Michel Marcus, Oct 12 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Mar 08 2013
EXTENSIONS
Verified there are no missing terms up to a(24) by Donovan Johnson, Apr 13 2013
a(25)-a(27) by Jud McCranie, Aug 31 2019
a(28)-a(32) by Jud McCranie, Oct 10 2019
STATUS
approved