A342006 - OEIS

%I #14 Mar 11 2021 21:07:23

%S 3,7,8,9,13,16,31,32,33,36,37,38,39,44,45,64,70,72,80,92,100,144,156,

%T 211,212,213,214,216,217,218,219,222,224,232,240,241,242,243,244,246,

%U 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

%N 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.

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

%H Antti Karttunen, <a href="/A342006/b342006.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%e 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.

%o (PARI)

%o A328114(n) = { my(s=0, p=2); while(n, s = max(s,(n%p)); n = n\p; p = nextprime(1+p)); (s); };

%o A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));

%o 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); };

%o A328391(n) = A051903(A327860(n));

%o isA342006(n) = (A328391(n) >= A328114(n));

%o (PARI) isA342006(n) = (0==A342005(n));

%Y Positions of zeros in A342005.

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

%K nonn,look

%O 1,1

%A _Antti Karttunen_, Mar 03 2021