A328391 - OEIS

%I #9 Oct 15 2019 17:21:51

%S 0,0,1,1,1,0,1,3,1,1,1,1,2,1,1,4,1,2,2,2,2,2,2,3,3,3,3,3,3,0,2,1,1,1,

%T 1,2,1,1,1,1,1,1,1,2,2,1,1,2,2,2,2,2,2,3,3,3,3,3,3,1,1,1,1,2,1,1,1,1,

%U 1,2,1,3,1,1,1,1,1,2,2,7,2,2,2,3,3,3,3,3,3,2,2,4,2,2,2,2,2,2,2,3,2,2,2,2,2

%N Maximal exponent in the prime factorization of A327860(n): a(n) = A051903(A327860(n)).

%H Antti Karttunen, <a href="/A328391/b328391.txt">Table of n, a(n) for n = 1..30030</a>

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

%F a(n) = A051903(A327860(n)) = A051903(A003415(A276086(n))).

%F a(A002110(n)) = 0 for all n >= 0.

%F For all n >= 1, a(n) >= A328114(n)-1. [Because arithmetic derivative will decrease the maximal prime exponent (A051903) of its argument by at most one]

%o (PARI)

%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));

%Y Cf. A002110, A003415, A051903, A276086, A327860, A327969, A328114, A328388, A328389, A328390, A328392.

%K nonn

%O 1,8

%A _Antti Karttunen_, Oct 15 2019