

A263940


Numbers such that the product of the sum of their antidivisors and the sum of the reciprocals of their antidivisors is an integer.


0




OFFSET

1,1


COMMENTS

A066466 is a subset of this sequence.
The sums are 1, 1, 1, 57, 1, 1457, 385, 1, ...


LINKS

Table of n, a(n) for n=1..8.


EXAMPLE

Antidivisors of 937 are 2, 3, 5, 15, 25, 75, 125, 375 and 625. Their sum is 1250 while the sum of their reciprocals is 1/2 + 1/3 + 1/5 + 1/15 + 1/25 + 1/75 + 1/125 + 1/375 + 1/625 = 1457/1250. Finally 1250 * 1457/1250 = 1457.


MAPLE

with(numtheory); P:=proc(q) local a, b, k, n;
for n from 3 to q do a:=0; b:=0;
for k from 2 to n1 do if abs((n mod k)k/2)<1 then a:=a+k; b:=b+1/k;
fi; od; if type(a*b, integer) then print(n); fi; od; end: P(10^4);


MATHEMATICA

f[n_] := Cases[Range[2, n  1], _?(Abs[Mod[n, #]  #/2] < 1 &)]; Select[Range[3, 3000], IntegerQ@ Times[Total@ f@ #, Total[1/f@ #]] &] (* Michael De Vlieger, Nov 11 2015 *)


CROSSREFS

Cf. A066272, A066466, A263928.
Sequence in context: A306493 A019209 A019120 * A256326 A239244 A267943
Adjacent sequences: A263937 A263938 A263939 * A263941 A263942 A263943


KEYWORD

nonn


AUTHOR

Paolo P. Lava, Oct 30 2015


STATUS

approved



