A258079 Numbers x such that (-1)sigma(x) | sigma(x) - x, where (-1)sigma(x) is defined in A049060 and sigma(x) - x is the sum of the aliquot parts of x (A001065).

1, 2, 6, 10, 36, 168, 1098, 1204, 2840, 19488, 1881124, 3105700, 445577184, 105314212224, 134633963520, 2167649138304

Offset: 1

Author

Paolo P. Lava, May 19 2015

Keywords

• nonn
• more

Comments

Ratio is equal to 1 for 2, 36, 1204, 2840, 1881124, 3105700, ...

a(17) > 10^13. - Hiroaki Yamanouchi, Sep 11 2015

Examples

			(-1)sigma(1) = 1, sigma(1) - 1 = 1 - 1 = 0 and 0 / 1 = 0;
(-1)sigma(2) = 1, sigma(2) - 2 = 3 - 2 = 1 and 1 / 1 = 1;
(-1)sigma(36) = 55, sigma(36) - 36 = 91 - 36 = 55 and 55 / 55 = 1; etc.
		

Crossrefs

Cf. A001065, A049060, A258077.

Programs

Maple

with(numtheory): P:=proc(q) local a,b,i,j,n; for n from 1 to q do a:=ifactors(n)[2]:
b:=1; for i from 1 to nops(a) do b:=b*(-1+sum(a[i][1]^j,j=1..a[i][2])): od:
if type((sigma(n)-n)/b,integer) then print(n); fi; od; end: P(10^6);

Extensions

a(13)-a(16) from Hiroaki Yamanouchi, Sep 11 2015