A342026 - OEIS

%I #16 Mar 14 2021 20:42:41

%S -1,-1,0,-1,-1,-1,0,2,0,-1,-1,-1,0,-1,-1,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,

%T -1,-1,-1,-1,-1,1,0,0,-1,-1,1,0,0,0,-1,-1,-1,-1,0,0,-1,-1,-1,-1,-1,-1,

%U -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,-1,-1,-1,-1,-1,0,-1,1,-1,-1,-1,-1,-1,-1,-1,4,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1

%N Difference in the maximal prime exponents between the arithmetic derivative of A276086(n) and A276086(n) itself, which is the prime product form of primorial base expansion of n.

%H Antti Karttunen, <a href="/A342026/b342026.txt">Table of n, a(n) for n = 1..65537</a>

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

%F a(n) = A328310(A276086(n)) = A328391(n) - A328114(n).

%F a(n) = -1 iff A342005(n) = 1.

%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) = if(!n,n,A051903(A327860(n)));

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

%o A342026(n) = (A328391(n) - A328114(n));

%Y Cf. A003415, A276086, A342005, A327860, A328114, A328310, A328391, A342006 (positions of nonnegative terms).

%Y Cf. also A342016, A342019.

%K sign

%O 1,8

%A _Antti Karttunen_, Mar 13 2021