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Numbers k for which A003415(k) is a multiple of A001414(k), where A003415 is the arithmetic derivative, and A001414 is the sum of prime factors with multiplicity.
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%I #10 Jun 08 2024 17:49:59

%S 1,4,6,8,9,10,14,15,16,21,22,25,26,27,32,33,34,35,36,38,39,46,49,51,

%T 55,57,58,62,64,65,69,72,74,77,81,82,85,86,87,91,93,94,95,100,106,111,

%U 112,115,118,119,121,122,123,125,126,128,129,133,134,141,142,143,145,146,155,156,158,159,161,166,169,177,178

%N Numbers k for which A003415(k) is a multiple of A001414(k), where A003415 is the arithmetic derivative, and A001414 is the sum of prime factors with multiplicity.

%H Antti Karttunen, <a href="/A373482/b373482.txt">Table of n, a(n) for n = 1..20000</a>

%t Select[Range[180],

%t Divisible[If[#1 < 2, 0, #1 Total[#2/#1 & @@@ #2]],

%t Total[Times @@@ #2]] & @@

%t {#, FactorInteger[#]} &] (* _Michael De Vlieger_, Jun 08 2024 *)

%o (PARI) isA373482 = A373481;

%Y Cf. A001414, A003415, A373481 (characteristic function).

%Y After the initial 1, positions of 0's in A373480.

%Y Subsequences: A176540 (k such that A003415(k) = A001414(k)), A346041.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 08 2024