A278234 - OEIS

%I #22 Jun 20 2017 23:27:21

%S 1,2,2,6,2,4,2,6,6,30,6,12,2,6,4,12,6,12,2,4,6,12,4,8,2,6,6,30,6,12,6,

%T 30,30,210,30,60,6,30,12,60,30,60,6,12,30,60,12,24,2,6,6,30,6,12,4,12,

%U 12,60,12,36,6,30,12,60,30,60,6,12,30,60,12,24,2,6,4,12,6,12,6,30,12,60,30,60,4,12,8,24,12,36,6,12,12,36,12,24,2,4,6,12,4,8,6

%N Filter-sequence for factorial base (digit slopes): Least number with the same prime signature as A275734(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(A275734(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="/A278234/b278234.txt">Table of n, a(n) for n = 0..40320</a>

%H Indranil Ghosh, <a href="/A278234/a278234_1.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(A275734(n)).

%F a(n) = A278235(A225901(n)).

%o (Scheme) (define (A278234 n) (A046523 (A275734 n)))

%Y Cf. A007623, A046523, A225901, A275734.

%Y Other filter-sequences related to factorial base: A278225, A278235, A278236.

%Y Sequences that partition N into same or coarser equivalence classes: A060130, A060502, A275811, A275946, A275962.

%K nonn

%O 0,2

%A _Antti Karttunen_, Nov 16 2016