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%I #27 Jun 20 2017 23:27:29
%S 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,
%T 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,
%U 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
%N Filter-sequence for factorial base (digit levels): Least number with the same prime signature as A275735(n).
%C 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 ...").
%C 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.
%H Antti Karttunen, <a href="/A278235/b278235.txt">Table of n, a(n) for n = 0..40320</a>
%H Indranil Ghosh, <a href="/A278235/a278235.txt">Python program for computing this sequence</a>
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F a(n) = A046523(A275735(n)).
%F a(n) = A278234(A225901(n)).
%o (Scheme) (define (A278235 n) (A046523 (A275735 n)))
%Y Cf. A046523, A225901, A275735.
%Y Other factorial base related filter-sequences: A278225, A278234, A278236.
%Y 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).
%K nonn
%O 0,2
%A _Antti Karttunen_, Nov 16 2016
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