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

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, 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, 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

Offset: 1

Author

Antti Karttunen, Mar 30 2019

Keywords

• nonn

Comments

Sum of digits when A108951(n) is written in primorial base (A049345).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..30030
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial base
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A001222, A002110, A034386, A049345, A108951, A276086, A276150, A324886.

Cf. A324383, A324386, A324387 (permutations of this sequence).

Programs

Mathematica

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 *)

PARI

A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
A276150(n) = { my(s=0,m); forprime(p=2, , if(!n, return(s)); m = n%p; s += m; n = (n-m)/p); };
A324888(n) = A276150(A108951(n));

Formula

a(n) = A276150(A108951(n)).

a(n) = A001222(A324886(n)).