A281685 Numbers k such that A001221(k) = A001221(A003415(k)).

4, 16, 18, 20, 21, 24, 26, 27, 33, 35, 38, 40, 44, 45, 48, 50, 51, 52, 56, 57, 62, 63, 65, 68, 69, 74, 75, 76, 77, 80, 85, 86, 91, 92, 93, 95, 96, 98, 99, 104, 106, 108, 111, 115, 117, 119, 122, 123, 126, 129, 133, 134, 135, 136, 141, 143, 144, 145, 146, 147

Offset: 1

Author

Colin Barker, Jan 27 2017

Keywords

• nonn

Comments

Numbers k such that the number of distinct prime divisors of k is equal to the number of distinct prime divisors of the arithmetic derivative of k.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001221, A003415, A209870, A281686.

Programs

Mathematica

a[n_] := If[Abs@n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[Abs@n]]];
Select[Range[100], PrimeNu[#] == PrimeNu[a[#]] &] (* G. C. Greubel, Apr 23 2017 *)

PARI

arde(n) = sum(i=1, #f=factor(n)~, n/f[1, i]*f[2, i])
select(k->omega(k)==omega(arde(k)), vector(200, k, k+1))