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A370114 Numbers k for which A276086(A003415(k)) is a multiple of k, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

%I A370114 #17 Feb 11 2024 14:19:58
%S A370114 1,2,6,10,15,42,50,70,98,105,245,294,330,343,375,726,770,825,1029,
%T A370114 1078,1155,1210,1375,1617,1694,1815,1925,2310,2450,2541,2662,2695,
%U A370114 3025,3822,3850,4290,4550,4719,5005,5145,5390,6125,6655,7098,7150,7546,7865,8450,8470,8575,8918,9317,9438,9555,10010,11319,11375
%N A370114 Numbers k for which A276086(A003415(k)) is a multiple of k, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
%C A370114 Numbers k that divide A327859(k). Sequence contains only terms of A048103 and does not contain any multiples of 9.
%H A370114 Antti Karttunen, <a href="/A370114/b370114.txt">Table of n, a(n) for n = 1..7501</a>
%o A370114 (PARI)
%o A370114 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A370114 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A370114 isA370114(n) = ((n>0) && !(A276086(A003415(n))%n));
%Y A370114 Fixed points of A369964. Positions of 1's in A370116.
%Y A370114 Intersection of A048103 and A369650 is a subsequence of this sequence. See the comments in latter.
%Y A370114 Cf. A003415, A276086, A327859, A370115.
%K A370114 nonn
%O A370114 1,2
%A A370114 _Antti Karttunen_, Feb 11 2024