A278235 Filter-sequence for factorial base (digit levels): Least number with the same prime signature as A275735(n).

1, 2, 2, 4, 2, 6, 2, 4, 4, 8, 6, 12, 2, 6, 6, 12, 4, 12, 2, 6, 6, 12, 6, 30, 2, 4, 4, 8, 6, 12, 4, 8, 8, 16, 12, 24, 6, 12, 12, 24, 12, 36, 6, 12, 12, 24, 30, 60, 2, 6, 6, 12, 4, 12, 6, 12, 12, 24, 12, 36, 4, 12, 12, 36, 8, 24, 6, 30, 30, 60, 12, 60, 2, 6, 6, 12, 6, 30, 6, 12, 12, 24, 30, 60, 6, 30, 30, 60, 12, 60, 4, 12, 12, 36, 12, 60, 2, 6, 6, 12, 6, 30, 6

Offset

0,2

Comments

This sequence can be used for filtering certain factorial base (A007623) related sequences, because it matches only with any such sequence b that can be computed as b(n) = f(A275735(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.

Links

Antti Karttunen, Table of n, a(n) for n = 0..40320

Indranil Ghosh, Python program for computing this sequence

Index entries for sequences computed from exponents in factorization of n

Index entries for sequences related to factorial base representation

Formula

a(n) = A046523(A275735(n)).

a(n) = A278234(A225901(n)).

Prog

(Scheme) (define (A278235 n) (A046523 (A275735 n)))

Crossrefs

Cf. A046523, A225901, A275735.

Other factorial base related filter-sequences: A278225, A278234, A278236.

Sequences that partition N into same or coarser equivalence classes: A060130, A257696 (?), A264990, A275806, A275948, A275964 (this is a proper a subset of the sequences that match with A278236).

Sequence in context: A086087 A284476 A082174 * A074369 A323407 A354875

Adjacent sequences: A278232 A278233 A278234 * A278236 A278237 A278238

Keyword

nonn

Author

Antti Karttunen, Nov 16 2016

Status

approved