A328572 Primorial base expansion of n converted into its prime product form, but with 1 subtracted from all nonzero digits: a(n) = A003557(A276086(n)).

1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 3, 3, 5, 5, 5, 5, 15, 15, 25, 25, 25, 25, 75, 75, 125, 125, 125, 125, 375, 375, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 3, 3, 5, 5, 5, 5, 15, 15, 25, 25, 25, 25, 75, 75, 125, 125, 125, 125, 375, 375, 7, 7, 7, 7, 21, 21, 7, 7, 7, 7, 21, 21, 35, 35, 35, 35, 105, 105, 175, 175, 175, 175, 525, 525, 875, 875, 875, 875

Offset: 0

Author

Antti Karttunen, Oct 20 2019

Keywords

• nonn
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 0..2310
• Antti Karttunen, Data supplement: n, a(n) computed for n = 0..32768
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003557, A051903, A085731, A276086, A327860, A328114, A328475, A328571, A328573, A328575, A328577.

Programs

Mathematica

Block[{b = MixedRadix[Reverse@ Prime@ Range@ 12]}, Array[#1/(Times @@ #2[[All, 1]]) & @@ {#1, FactorInteger[#]} &[Times @@ Power @@@ #] &@ Transpose@ {Prime@ Range@ Length@ #, Reverse@ #} &@ IntegerDigits[#, b] &, 87, 0]] (* Michael De Vlieger, Mar 12 2021 *)

PARI

A328572(n) = { my(m=1, p=2); while(n, if(n%p, m *= p^((n%p)-1)); n = n\p; p = nextprime(1+p)); (m); };

Formula

a(n) = A003557(A276086(n)).

a(n) = A276086(n) / A328571(n).

a(n) = A328475(n) / A328573(n).

For all n >= 1, 1+A051903(a(n)) = A328114(n).

a(n) = A085731(A276086(n)) = gcd(A276086(n), A327860(n)). - Antti Karttunen, Feb 28 2021