A248816 Numbers that are equal to the arithmetic derivative of the sum of their aliquot parts.

152, 284, 4316, 18632, 25484, 2657259, 8394752, 12186976, 17702756, 1172473731, 2147581952, 13716855652, 63831498112

Offset: 1

Author

Paolo P. Lava, Oct 15 2014

Keywords

• nonn
• more

Comments

Solutions of the equations n = (sigma(n)-n)'.

a(12) > 5*10^9. - Michel Marcus, Nov 01 2014

There could be a relation with terms in A125246 and A228450, since some terms of these sequences are here also. - Michel Marcus, Oct 30 2014

a(14) > 10^11. - Giovanni Resta, May 29 2016

Examples

			Sum of the aliquot parts of 284 is sigma(284) - 284 = 220 and the arithmetic derivative of 220 is 284.~
		

Crossrefs

Cf. A000203, A003415, A230164.

Programs

Maple

with(numtheory): P:= proc(q) local a,n,p; for n from 1 to q do
a:=(sigma(n)-n)*add(op(2,p)/op(1,p),p=ifactors(sigma(n)-n)[2]);
if n=a then print(n); fi; od; end: P(10^9);

PARI

ad(n) = sum(i=1, #f=factor(n)~, n/f[1, i]*f[2, i]);
isok(n) = ad(sigma(n) - n) == n; \\ Michel Marcus, Oct 28 2014

Extensions

a(6)-a(11) from Michel Marcus, Oct 28 2014

a(12)-a(13) from Giovanni Resta, May 29 2016