cp's OEIS Frontend

A324888 Minimal number of primorials (A002110) that add to A108951(n).

%I A324888 #9 Nov 18 2019 22:07:19
%S A324888 1,1,1,2,1,2,1,2,2,2,1,4,1,2,6,4,1,4,1,4,6,2,1,4,6,2,2,4,1,6,1,2,6,2,
%T A324888 10,8,1,2,6,2,1,2,1,4,6,2,1,4,8,12,6,4,1,4,6,8,6,2,1,6,1,2,6,4,14,12,
%U A324888 1,4,6,10,1,6,1,2,10,4,18,12,1,4,8,2,1,4,12,2,6,8,1,12,18,4,6,2,8,8,1,16,12,8,1,12,1,8,8
%N A324888 Minimal number of primorials (A002110) that add to A108951(n).
%C A324888 Sum of digits when A108951(n) is written in primorial base (A049345).
%H A324888 Antti Karttunen, <a href="/A324888/b324888.txt">Table of n, a(n) for n = 1..30030</a>
%H A324888 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A324888 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A324888 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A324888 a(n) = A276150(A108951(n)).
%F A324888 a(n) = A001222(A324886(n)).
%t A324888 With[{b = Reverse@ Prime@ Range@ 120}, Array[Total@ 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 A324888 (PARI)
%o A324888 A034386(n) = prod(i=1, primepi(n), prime(i));
%o A324888 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
%o A324888 A276150(n) = { my(s=0,m); forprime(p=2, , if(!n, return(s)); m = n%p; s += m; n = (n-m)/p); };
%o A324888 A324888(n) = A276150(A108951(n));
%Y A324888 Cf. A001222, A002110, A034386, A049345, A108951, A276086, A276150, A324886.
%Y A324888 Cf. A324383, A324386, A324387  (permutations of this sequence).
%K A324888 nonn
%O A324888 1,4
%A A324888 _Antti Karttunen_, Mar 30 2019