A263940 Numbers such that the product of the sum of their anti-divisors and the sum of the reciprocals of their anti-divisors is an integer.

3, 4, 6, 37, 96, 937, 2760, 393216

Offset: 1

Author

Paolo P. Lava, Oct 30 2015

Keywords

• nonn

Comments

A066466 is a subset of this sequence.

The sums are 1, 1, 1, 57, 1, 1457, 385, 1, ...

Examples

			Anti-divisors 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.
		

Crossrefs

Cf. A066272, A066466, A263928.

Programs

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 n-1 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 *)