A239726 Numbers n such that sigma(n) - n = sigma(n') - n', where n' is the arithmetic derivative of n.

1, 4, 27, 369, 2120, 2853, 3125, 6620, 24932, 65588, 210404, 245444, 347049, 823543, 833444, 968204, 1610684, 3125492, 5046044, 5856308, 9339020, 9900236, 10614092, 10636772, 11421164, 11617772, 13276892, 16116764, 16244156, 18422444, 21073916, 21656564

Offset

1,2

Comments

A051674 is a subset of this sequence.

Links

Table of n, a(n) for n=1..32.

Example

Arithmetic derivative of 369 is 255, sigma(369) = 546, sigma(255) = 432 and 546 - 369 = 432 - 255 = 177.

Maple

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

Crossrefs

Cf. A000005, A003415, A051674, A239940.

Sequence in context: A304654 A203202 A320961 * A058155 A334527 A104169

Adjacent sequences: A239723 A239724 A239725 * A239727 A239728 A239729

Keyword

nonn

Author

Paolo P. Lava, Mar 31 2014

Extensions

a(18)-a(32) from Giovanni Resta, Mar 31 2014

Status

approved