A369958 Numbers k such that A003415(k)/gcd(k, A003415(k)) >= A276086(k)/gcd(k, A276086(k)), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

6, 30, 33, 42, 63, 210, 212, 213, 214, 220, 420, 429, 462, 2310, 2312, 2313, 2314, 2315, 2316, 2317, 2318, 2319, 2320, 2325, 2330, 2340, 2342, 2343, 2344, 2345, 2346, 2355, 2370, 2373, 2379, 2380, 2520, 2522, 2526, 2530, 2535, 2552, 2730, 3003, 4620, 4622, 4623, 4626, 4628, 4630, 4654, 4680, 4830, 4836, 4862, 6930, 6942, 7150

Offset: 1

Author

Antti Karttunen, Feb 07 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..13305 (terms up to 3*A002110(9))

Crossrefs

Cf. A003415, A083345, A276086, A351251.

Subsequences: A002110 (after its two initial terms), A369959, A369960.

Cf. also A351228.

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); };
isA369958(n) = ((A003415(n)/gcd(n, A003415(n))) >= (A276086(n)/gcd(n, A276086(n))));

Formula

{k | A083345(k) >= A351251(k)}.