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A369959 Numbers k such that A003415(k) >= A276086(k) and gcd(k, A003415(k)) = gcd(k, A276086(k)), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

%I A369959 #8 Feb 07 2024 20:39:30
%S A369959 6,30,210,214,2310,2313,2315,2317,2318,2342,2346,2370,2526,4622,4830,
%T A369959 30030,30031,30033,30034,30035,30038,30041,30043,30046,30054,30061,
%U A369959 30062,30066,30069,30074,30094,30098,30102,30242,30245,30247,30249,30254,30270,30274,30282,32342,32345,32347,32350,32354,32374,32553,60062
%N A369959 Numbers k such that A003415(k) >= A276086(k) and gcd(k, A003415(k)) = gcd(k, A276086(k)), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
%H A369959 Antti Karttunen, <a href="/A369959/b369959.txt">Table of n, a(n) for n = 1..3195</a>
%H A369959 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A369959 {k | A085731(n) == A324198(n) and A083345(k) >= A351251(k)}.
%o A369959 (PARI)
%o A369959 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A369959 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A369959 isA369959(n) = { my(t=A003415(n), u=A276086(n), g=gcd(n,t), h=gcd(n,u)); ((g==h) && ((t/g) >= (u/h))); };
%Y A369959 Intersection of A351228 and A369962.
%Y A369959 Subsequence of A369958.
%Y A369959 Cf. A003415, A083345, A085731, A276086, A324198, A351251, A369960 (subsequence).
%K A369959 nonn
%O A369959 1,1
%A A369959 _Antti Karttunen_, Feb 07 2024