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).

6, 213, 214, 2315, 2317, 2319, 2342, 2343, 2348, 2349, 2372, 2523, 2524, 2526, 2552, 4622, 4623, 4628, 4652, 6932, 6936, 6960, 30041, 30043, 30046, 30052, 30054, 30062, 30074, 30075, 30076, 30093, 30094, 30098, 30100, 30102, 30150, 30242, 30245, 30249, 30254, 30256, 30258, 30273, 30274, 30282, 32343, 32345, 32347

Offset: 1

Author

Antti Karttunen, Feb 22 2024

Keywords

• nonn

Comments

Numbers k such that A003415(k) >= A276086(k) >= s * k^((s-1)/s), with s = A001222(k).

See comments in A370127.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..6439

Crossrefs

Setwise difference A351228 \ A370127.

Cf. A001222, A003415, A276086.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
isA370128(n) = { my(x=A276086(n), s=bigomega(n)); ((x<=A003415(n)) && ((x/s)^s >= n^(s-1))); };