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Numbers k for which k is a multiple of A276086(A003415(k)), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
4

%I #14 Feb 11 2024 14:20:04

%S 0,1,2,10,15,161,2189,5005,27030,29861,510221,223092341

%N Numbers k for which k is a multiple of A276086(A003415(k)), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

%C Question: Is the squarefreeness a necessary condition for the nonzero terms of this sequence?

%C Many of the terms occur also in A368703, because the arithmetic derivative of those terms is one of the primorial numbers, A002110.

%C If it exists, a(13) > 1241513984.

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o isA370115(n) = !(n%A276086(A003415(n)));

%Y Positions of 1's in A370117, positions of 0's in A370120.

%Y Intersection of A048103 and A369650 is a subsequence of this sequence. See the comments in latter.

%Y Cf. A002110, A003415, A276086, A327859, A368703.

%Y Cf. also A369970, A370114.

%K nonn

%O 1,3

%A _Antti Karttunen_, Feb 11 2024