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%I #24 Nov 19 2016 08:28:16
%S 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,
%T 48,48,240,144,720,2,6,6,30,12,60,6,30,30,210,60,420,12,60,60,420,180,
%U 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
%N Filter-sequence for primorial base: least number with the same prime signature as A276086(n).
%C 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 ...").
%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.
%C 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.
%H Antti Karttunen, <a href="/A278226/b278226.txt">Table of n, a(n) for n = 0..30030</a>
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F a(n) = A046523(A276086(n)).
%o (Scheme) (define (A278226 n) (A046523 (A276086 n)))
%Y Cf. A046523, A049345, A276086.
%Y Cf. also A278243.
%Y Similar sequences: A278222 (base-2 related), A069877 (base-10), A278236 (factorial base).
%Y Differs from A278236 for the first time at n=24, where a(24)=16, while A278236(24)=2.
%Y Sequences that partition N into same or coarser equivalence classes: A267263, A276150.
%K nonn,base
%O 0,2
%A _Antti Karttunen_, Nov 16 2016
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