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%I #11 Nov 18 2019 22:18:21
%S 1,1,1,2,1,2,1,1,1,2,1,4,1,2,6,2,1,2,1,4,6,2,1,3,4,2,1,4,1,5,1,1,6,2,
%T 8,4,1,2,6,1,1,1,1,4,5,2,1,3,6,8,6,4,1,2,4,8,6,2,1,3,1,2,3,2,13,12,1,
%U 4,6,5,1,3,1,2,5,4,16,12,1,2,6,2,1,2,11,2,6,8,1,10,12,4,6,2,7,6,1,12,10,6,1,12,1,8,4
%N Number of times most frequent primorial is present in the greedy sum of primorials adding to A108951(n).
%C The greedy sum is also the sum with the minimal number of primorials, used for example in the primorial base representation.
%H Antti Karttunen, <a href="/A329344/b329344.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F a(n) = A328114(A108951(n)) = A051903(A324886(n)).
%e For n = 24 = 2^3 * 3, A108951(24) = A034386(2)^3 * A034386(3) = 2^3 * 6 = 48 = 30 + 6 + 6 + 6, and as the most frequent primorial in the sum is 6 = A002110(2), we have a(24) = 3.
%t 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}]] &, 105] ] (* _Michael De Vlieger_, Nov 18 2019 *)
%o (PARI)
%o A034386(n) = prod(i=1, primepi(n), prime(i));
%o A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) }; \\ From A108951
%o A328114(n) = { my(s=0, p=2); while(n, s = max(s,(n%p)); n = n\p; p = nextprime(1+p)); (s); };
%o A329344(n) = A328114(A108951(n));
%o (PARI)
%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A324886(n) = A276086(A108951(n));
%o A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));
%o A329344(n) = A051903(A324886(n));
%Y Cf. A002110, A034386, A051903, A108951, A276086, A324886, A324888, A328114, A329040, A329045, A329343, A329348, A329349.
%K nonn
%O 1,4
%A _Antti Karttunen_, Nov 11 2019
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