A369959 Numbers k such that A003415(k) >= A276086(k) and gcd(k, A003415(k)) = gcd(k, A276086(k)), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

6, 30, 210, 214, 2310, 2313, 2315, 2317, 2318, 2342, 2346, 2370, 2526, 4622, 4830, 30030, 30031, 30033, 30034, 30035, 30038, 30041, 30043, 30046, 30054, 30061, 30062, 30066, 30069, 30074, 30094, 30098, 30102, 30242, 30245, 30247, 30249, 30254, 30270, 30274, 30282, 32342, 32345, 32347, 32350, 32354, 32374, 32553, 60062

Offset: 1

Author

Antti Karttunen, Feb 07 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..3195
• Index entries for sequences related to primorial base

Crossrefs

Intersection of A351228 and A369962.

Subsequence of A369958.

Cf. A003415, A083345, A085731, A276086, A324198, A351251, A369960 (subsequence).

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); };
isA369959(n) = { my(t=A003415(n), u=A276086(n), g=gcd(n,t), h=gcd(n,u)); ((g==h) && ((t/g) >= (u/h))); };

Formula

{k | A085731(n) == A324198(n) and A083345(k) >= A351251(k)}.