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

30, 32, 36, 60, 210, 212, 216, 240, 420, 2310, 2312, 2313, 2314, 2316, 2318, 2320, 2322, 2324, 2328, 2340, 2344, 2346, 2352, 2370, 2376, 2400, 2520, 2522, 2528, 2550, 2730, 4620, 4624, 4626, 4632, 4650, 4656, 4680, 4830, 4832, 4860, 6930, 30030, 30031, 30032, 30033, 30034, 30035, 30036, 30037, 30038, 30039, 30040

Offset: 1

Author

Antti Karttunen, Feb 22 2024

Keywords

• nonn

Comments

Numbers k such that A276086(k) < s * k^((s-1)/s), with s = A001222(k).

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}.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..5204
• Victor Ufnarovski and Bo Åhlander, How to Differentiate a Number, J. Integer Seqs., Vol. 6, 2003, #03.3.4.

Crossrefs

Setwise difference A351228 \ A370128.

Cf. A001222, A003415, A276086.

Cf. A066576 (subsequence).

Programs

PARI

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
isA370127(n) = { my(x=A276086(n), s=bigomega(n)); ((x/s)^s < n^(s-1)); };