cp's OEIS Frontend

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.

%I A342006 #14 Mar 11 2021 21:07:23
%S A342006 3,7,8,9,13,16,31,32,33,36,37,38,39,44,45,64,70,72,80,92,100,144,156,
%T A342006 211,212,213,214,216,217,218,219,222,224,232,240,241,242,243,244,246,
%U A342006 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 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.
%C A342006 Numbers k for which A328391(k) >= A328114(k).
%H A342006 Antti Karttunen, <a href="/A342006/b342006.txt">Table of n, a(n) for n = 1..10000</a>
%H A342006 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%e A342006 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 A342006 (PARI)
%o A342006 A328114(n) = { my(s=0, p=2); while(n, s = max(s,(n%p)); n = n\p; p = nextprime(1+p)); (s); };
%o A342006 A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));
%o A342006 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 A342006 A328391(n) = A051903(A327860(n));
%o A342006 isA342006(n) = (A328391(n) >= A328114(n));
%o A342006 (PARI) isA342006(n) = (0==A342005(n));
%Y A342006 Positions of zeros in A342005.
%Y A342006 Cf. A003415, A051903, A276086, A327860, A328114, A328391, A342004, A342018.
%K A342006 nonn,look
%O A342006 1,1
%A A342006 _Antti Karttunen_, Mar 03 2021