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A329619 Difference between the maximal digit value used when A108951(n) is written in primorial base and its 2-adic valuation.

%I A329619 #13 Nov 18 2019 22:04:25
%S A329619 1,0,0,0,0,0,0,-2,-1,0,0,1,0,0,4,-2,0,-1,0,1,4,0,0,-1,2,0,-2,1,0,2,0,
%T A329619 -4,4,0,6,0,0,0,4,-3,0,-2,0,1,2,0,0,-2,4,5,4,1,0,-2,2,4,4,0,0,-1,0,0,
%U A329619 0,-4,11,9,0,1,4,2,0,-2,0,0,2,1,14,9,0,-3,2,0,0,-2,9,0,4,4,0,6,10,1,4,0,5,0,0,9,7,2,0,9,0,4,1
%N A329619 Difference between the maximal digit value used when A108951(n) is written in primorial base and its 2-adic valuation.
%H A329619 Antti Karttunen, <a href="/A329619/b329619.txt">Table of n, a(n) for n = 1..65537</a>
%H A329619 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A329619 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A329619 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A329619 a(n) = A329344(n) - A001222(n).
%F A329619 a(n) = A328114(A108951(n)) - A007814(A108951(n)).
%F A329619 a(p) = 0 for all primes p.
%t A329619 With[{b = Reverse@ Prime@ Range@ 120}, Array[Max@ IntegerDigits[#, MixedRadix[b]] &@ Apply[Times, Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Times @@ Prime@ Range@ PrimePi@ p, e}]] - PrimeOmega[#] &, 105] ] (* _Michael De Vlieger_, Nov 18 2019 *)
%o A329619 (PARI)
%o A329619 A034386(n) = prod(i=1, primepi(n), prime(i));
%o A329619 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
%o A329619 A328114(n) = { my(s=0, p=2); while(n, s = max(s,(n%p)); n = n\p; p = nextprime(1+p)); (s); };
%o A329619 A329344(n) = A328114(A108951(n));
%o A329619 A329619(n) = (A329344(n) - bigomega(n));
%Y A329619 Cf. A001222, A007814, A034386, A108951, A276086, A324886, A328114, A329344, A329618, A329620, A329622.
%K A329619 sign
%O A329619 1,8
%A A329619 _Antti Karttunen_, Nov 18 2019