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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.
6
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).
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); };
isA342006(n) = (A328391(n) >= A328114(n));
(PARI) isA342006(n) = (0==A342005(n));
CROSSREFS
Positions of zeros in A342005.
Sequence in context: A096079 A298984 A094551 * A239937 A375019 A114441
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, Mar 03 2021
STATUS
approved