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A370127 Numbers k such that (A276086(k)/s)^s < k^(s-1), where A276086 is the primorial base exp-function, and s = bigomega(k).

%I A370127 #14 Feb 22 2024 20:09:17
%S A370127 30,32,36,60,210,212,216,240,420,2310,2312,2313,2314,2316,2318,2320,
%T A370127 2322,2324,2328,2340,2344,2346,2352,2370,2376,2400,2520,2522,2528,
%U A370127 2550,2730,4620,4624,4626,4632,4650,4656,4680,4830,4832,4860,6930,30030,30031,30032,30033,30034,30035,30036,30037,30038,30039,30040
%N A370127 Numbers k such that (A276086(k)/s)^s < k^(s-1), where A276086 is the primorial base exp-function, and s = bigomega(k).
%C A370127 Numbers k such that A276086(k) < s * k^((s-1)/s), with s = A001222(k).
%C A370127 For these numbers it must hold that A276086(k) < A003415(k) because (A003415(k)/s)^s >= k^(s-1) [with s = A001222(k)] holds for all k >= 2. See Ufnarovski and Åhlander, Theorem 9, point (4). In other words, this is a subsequence of A351228 \ {6}.
%H A370127 Antti Karttunen, <a href="/A370127/b370127.txt">Table of n, a(n) for n = 1..5204</a>
%H A370127 Victor Ufnarovski and Bo Åhlander, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL6/Ufnarovski/ufnarovski.html">How to Differentiate a Number</a>, J. Integer Seqs., Vol. 6, 2003, #03.3.4.
%o A370127 (PARI)
%o A370127 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A370127 isA370127(n) = { my(x=A276086(n), s=bigomega(n)); ((x/s)^s < n^(s-1)); };
%Y A370127 Setwise difference A351228 \ A370128.
%Y A370127 Cf. A001222, A003415, A276086.
%Y A370127 Cf. A066576 (subsequence).
%K A370127 nonn
%O A370127 1,1
%A A370127 _Antti Karttunen_, Feb 22 2024