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Numbers k such that k' = sigma(k) - phi(k), where k' = A003415(k) is the arithmetic derivative of k.
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%I #11 Jul 14 2021 10:03:59

%S 1,88,1104,492624,30818736,200827760,1598249556,4575586644,8491046375,

%T 8554970196,29917317500,54481242640,202195886375,3201891498000

%N Numbers k such that k' = sigma(k) - phi(k), where k' = A003415(k) is the arithmetic derivative of k.

%C a(15) > 10^13.

%t ad[1]=0; ad[n_]:=n*Total[(#1[[2]] / #1[[1]]&) /@ FactorInteger[n]]; Select[Range[500000], ad[#] == DivisorSigma[1,#] - EulerPhi[#] &]

%Y Cf. A000010, A000203, A003415, A166374, A230164.

%K nonn

%O 1,2

%A _Giovanni Resta_, Mar 13 2014