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%I #23 Jan 14 2024 17:28:51
%S 4,8,24,27,32,36,40,48,54,56,60,64,72,80,84,88,96,100,104,112,120,128,
%T 132,135,136,140,152,156,162,168,176,184,196,200,204,216,220,224,228,
%U 232,243,248,260,264,270,272,276,280,288,296,304,308,312,324,328,340,344,348,351,352,360,364,368,372,376,378,380
%N Numbers k for which there is no prime p such that p^p divides A342001(k), but for A003415(k) such a prime exists. Here A003415(n) is the arithmetic derivative of n, and A342001(n) = A003415(n) / A003557(n).
%C Numbers k such that A342001(k) is in A048103, but A003415(k) is in its complement A100716. The condition implies that k itself is in A100716.
%C The converse case, where p^p divides A342001(k) but not A003415(k), is not possible because the former is a divisor of the latter.
%e For n = 27 = 3^3, A003415(27) = 27, and A342001(27) = 3, thus as 3^3 divides the former, but not the latter, 27 is included in this sequence.
%o (PARI) \\ See A368913.
%Y Setwise difference A368904 \ A358215. Subsequence of A100716.
%Y Cf. A003415, A048103, A342001, A359550.
%Y Cf. A368913 (characteristic function).
%K nonn
%O 1,1
%A _Antti Karttunen_, Jan 09 2024