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A377989 Numbers k such that A003415(A276085(k)) has no p^p-factors, where A003415 is the arithmetic derivative, and A276085 is fully additive with a(p) = p#/p.

%I A377989 #14 Mar 31 2025 01:46:24
%S A377989 3,4,5,6,7,8,10,11,13,14,17,18,19,22,23,24,26,27,29,30,31,32,36,37,38,
%T A377989 40,41,42,43,45,47,48,50,53,54,56,59,60,61,63,64,66,67,70,71,72,73,74,
%U A377989 75,78,79,80,82,83,84,86,88,89,90,96,97,98,99,100,101,103,104,105,106,107,109,110,112,113,114,117,118,120
%N A377989 Numbers k such that A003415(A276085(k)) has no p^p-factors, where A003415 is the arithmetic derivative, and A276085 is fully additive with a(p) = p#/p.
%C A377989 Numbers k such that A373842(k) is in A048103.
%C A377989 Odd primes (A065091) are all present. See comment in A024451.
%e A377989 A276085(1) = 0 and A276085(2) = 1, and as A003415(0) = A003415(1) = 0, and because 0 is a multiple of every number of the form p^p, with p prime, 1 and 2 are NOT included in this sequence.
%e A377989 A276085(3) = 2, A003415(2) = 1, and as 1 has no p^p-factors, 3 is included in this sequence.
%e A377989 A276085(34) = 30031 = A002110(1-1)+A002110(7-1) (34 = 2*17 = prime(1)*prime(7)), and because A003415(30031) = 568 = 2^2 * 2 * 71, with a factor of the form p^p, 34 is NOT included in this sequence.
%o A377989 (PARI) isA377989 = A377988;
%Y A377989 Cf. A003415, A024451, A048103, A065091 (subsequence), A276085, A359550, A368915, A373842,  A377988 (characteristic function).
%Y A377989 Subsequence of A377869. First terms there, but not present here are 2 and 34.
%K A377989 nonn
%O A377989 1,1
%A A377989 _Antti Karttunen_, Nov 18 2024