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A373482 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.

%I A373482 #10 Jun 08 2024 17:49:59
%S A373482 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 A373482 55,57,58,62,64,65,69,72,74,77,81,82,85,86,87,91,93,94,95,100,106,111,
%U A373482 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 A373482 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 A373482 Antti Karttunen, <a href="/A373482/b373482.txt">Table of n, a(n) for n = 1..20000</a>
%t A373482 Select[Range[180],
%t A373482   Divisible[If[#1 < 2, 0, #1  Total[#2/#1 & @@@ #2]],
%t A373482     Total[Times @@@ #2]] & @@
%t A373482   {#, FactorInteger[#]} &] (* _Michael De Vlieger_, Jun 08 2024 *)
%o A373482 (PARI) isA373482 = A373481;
%Y A373482 Cf. A001414, A003415, A373481 (characteristic function).
%Y A373482 After the initial 1, positions of 0's in A373480.
%Y A373482 Subsequences: A176540 (k such that A003415(k) = A001414(k)), A346041.
%K A373482 nonn
%O A373482 1,2
%A A373482 _Antti Karttunen_, Jun 08 2024