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A370128 Numbers k such that (A276086(k)/s)^s >= k^(s-1) and A276086(k) <= A003415(k), where A003415 is the arithmetic derivative, A276086 is the primorial base exp-function, and s = bigomega(k).

%I A370128 #11 Feb 22 2024 17:46:00
%S A370128 6,213,214,2315,2317,2319,2342,2343,2348,2349,2372,2523,2524,2526,
%T A370128 2552,4622,4623,4628,4652,6932,6936,6960,30041,30043,30046,30052,
%U A370128 30054,30062,30074,30075,30076,30093,30094,30098,30100,30102,30150,30242,30245,30249,30254,30256,30258,30273,30274,30282,32343,32345,32347
%N A370128 Numbers k such that (A276086(k)/s)^s >= k^(s-1) and A276086(k) <= A003415(k), where A003415 is the arithmetic derivative, A276086 is the primorial base exp-function, and s = bigomega(k).
%C A370128 Numbers k such that A003415(k) >= A276086(k) >= s * k^((s-1)/s), with s = A001222(k).
%C A370128 See comments in A370127.
%H A370128 Antti Karttunen, <a href="/A370128/b370128.txt">Table of n, a(n) for n = 1..6439</a>
%o A370128 (PARI)
%o A370128 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A370128 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A370128 isA370128(n) = { my(x=A276086(n), s=bigomega(n)); ((x<=A003415(n)) && ((x/s)^s >= n^(s-1))); };
%Y A370128 Setwise difference A351228 \ A370127.
%Y A370128 Cf. A001222, A003415, A276086.
%K A370128 nonn
%O A370128 1,1
%A A370128 _Antti Karttunen_, Feb 22 2024