A239726 - OEIS

%I #16 Oct 21 2014 03:20:19

%S 1,4,27,369,2120,2853,3125,6620,24932,65588,210404,245444,347049,

%T 823543,833444,968204,1610684,3125492,5046044,5856308,9339020,9900236,

%U 10614092,10636772,11421164,11617772,13276892,16116764,16244156,18422444,21073916,21656564

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

%C A051674 is a subset of this sequence.

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

%p with(numtheory); P:=proc(q) local a,n,p;

%p for n from 1 to q do a:=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]);

%p if sigma(a)-a=sigma(n)-n then print(n); fi;

%p od; end: P(10^9);

%Y Cf. A000005, A003415, A051674, A239940.

%K nonn

%O 1,2

%A _Paolo P. Lava_, Mar 31 2014

%E a(18)-a(32) from _Giovanni Resta_, Mar 31 2014