A278226 Filter-sequence for primorial base: least number with the same prime signature as A276086(n).

1, 2, 2, 6, 4, 12, 2, 6, 6, 30, 12, 60, 4, 12, 12, 60, 36, 180, 8, 24, 24, 120, 72, 360, 16, 48, 48, 240, 144, 720, 2, 6, 6, 30, 12, 60, 6, 30, 30, 210, 60, 420, 12, 60, 60, 420, 180, 1260, 24, 120, 120, 840, 360, 2520, 48, 240, 240, 1680, 720, 5040, 4, 12, 12, 60, 36, 180, 12, 60, 60, 420, 180, 1260, 36, 180, 180, 1260, 900, 6300, 72, 360, 360, 2520, 1800

Offset: 0

Author

Antti Karttunen, Nov 16 2016

Keywords

• nonn
• base

Comments

This sequence can be used for filtering certain primorial base related sequences, because it matches only with any such sequence b that can be computed as b(n) = f(A276086(n)), where f(n) is any function that depends only on the prime signature of n (some of these are listed under the index entry for "sequences computed from exponents in ...").

Matching in this context means that the sequence a matches with the sequence b iff for all i, j: a(i) = a(j) => b(i) = b(j). In other words, iff the sequence b partitions the natural numbers to the same or coarser equivalence classes (as/than the sequence a) by the distinct values it obtains.

Any such sequence should match where the result is computed from the nonzero digits (that may also be > 9) in the primorial base representation of n, but does not depend on their order. Some of these are listed on the last line of the Crossrefs section.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..30030
• Index entries for sequences computed from exponents in factorization of n
• Index entries for sequences related to primorial base

Crossrefs

Cf. A046523, A049345, A276086.

Cf. also A278243.

Similar sequences: A278222 (base-2 related), A069877 (base-10), A278236 (factorial base).

Differs from A278236 for the first time at n=24, where a(24)=16, while A278236(24)=2.

Sequences that partition N into same or coarser equivalence classes: A267263, A276150.

Programs

Scheme

(define (A278226 n) (A046523 (A276086 n)))

Formula

a(n) = A046523(A276086(n)).