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

1,1

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to primorial base

Example

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.

Prog

(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));

Crossrefs

Positions of zeros in A342005.

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

Sequence in context: A096079 A298984 A094551 * A239937 A375019 A114441

Adjacent sequences: A342003 A342004 A342005 * A342007 A342008 A342009

Keyword

nonn,look

Author

Antti Karttunen, Mar 03 2021

Status

approved