A342006 Numbers k where the maximal prime exponent in the arithmetic derivative of A276086(k) attains the maximal exponent in A276086(k), where A276086 gives the prime product form of primorial base expansion of its argument.

3, 7, 8, 9, 13, 16, 31, 32, 33, 36, 37, 38, 39, 44, 45, 64, 70, 72, 80, 92, 100, 144, 156, 211, 212, 213, 214, 216, 217, 218, 219, 222, 224, 232, 240, 241, 242, 243, 244, 246, 247, 248, 249, 252, 253, 271, 272, 280, 287, 288, 296, 300, 303, 308, 316, 348, 388, 424, 432, 440, 448, 450, 452, 460, 462, 480, 488, 493, 496

Offset: 1

Author

Antti Karttunen, Mar 03 2021

Keywords

• nonn
• look

Comments

Numbers k for which A328391(k) >= A328114(k).

Examples

			16 is present as A276086(16) = 225, A003415(225) = 240 = 2^4 * 3 * 5, with maximum exponent = 4 >= the maximal exponent 4 in 16 = 2^4.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to primorial base

Crossrefs

Positions of zeros in A342005.

Cf. A003415, A051903, A276086, A327860, A328114, A328391, A342004, A342018.

Programs

PARI

A328114(n) = { my(s=0, p=2); while(n, s = max(s,(n%p)); n = n\p; p = nextprime(1+p)); (s); };
A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));
A327860(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
A328391(n) = A051903(A327860(n));
isA342006(n) = (A328391(n) >= A328114(n));

PARI

isA342006(n) = (0==A342005(n));