# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a278236
Showing 1-1 of 1

%I A278236 #41 Feb 07 2024 01:18:57
%S A278236 1,2,2,6,4,12,2,6,6,30,12,60,4,12,12,60,36,180,8,24,24,120,72,360,2,6,
%T A278236 6,30,12,60,6,30,30,210,60,420,12,60,60,420,180,1260,24,120,120,840,
%U A278236 360,2520,4,12,12,60,36,180,12,60,60,420,180,1260,36,180,180,1260,900,6300,72,360,360,2520,1800,12600,8,24,24,120,72,360,24,120,120,840,360,2520
%N A278236 Filter-sequence for factorial base (digit values): least number with the same prime signature as A276076(n).
%C A278236 This sequence can be used for filtering certain factorial base related sequences, because it matches only with any such sequence b that can be computed as b(n) = f(A276076(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 A278236 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 A278236 Any such sequence should match where the result is computed from the nonzero digits (that may also be > 9) in the factorial base representation of n, but does not depend on their order. Some of these are listed on the last line of the Crossrefs section.
%C A278236 Note that as A275735 is present in that list it means that the sequences matching to its filter-sequence A278235 form a subset of the sequences matching to this sequence. Also, for A275735 there is a stronger condition that for any i, j: a(i) = a(j) <=> A275735(i) = A275735(j), which if true, would imply that there is an injective function f such that f(A275735(n)) = A278236(n), and indeed, this function seems to be A181821.
%H A278236 Antti Karttunen, <a href="/A278236/b278236.txt">Table of n, a(n) for n = 0..40320</a>
%H A278236 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%H A278236 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
%F A278236 a(n) = A046523(A276076(n)).
%F A278236 a(n) = A181821(A275735(n)). [Empirical formula found with the help of equivalence class matching. Not yet proved.]
%t A278236 a[n_] := Module[{k = n, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; s = ReverseSort[s]; Times @@ (Prime[Range[Length[s]]] ^ s)]; Array[a, 100, 0] (* _Amiram Eldar_, Feb 07 2024 *)
%o A278236 (Scheme) (define (A278236 n) (A046523 (A276076 n)))
%Y A278236 Cf. A007623, A046523, A181821, A276076.
%Y A278236 Similar sequences: A278222 (base-2 related), A069877 (base-10), A278226 (primorial base), A278225, A278234, A278235 (other variants for factorial base),
%Y A278236 Differs from A278226 for the first time at n=24, where a(24)=2, while A278226(24)=16.
%Y A278236 Sequences that partition N into same or coarser equivalence classes: A275735 (<=>), A034968, A060130, A227153, A227154, A246359, A257079, A257511, A257679, A257694, A257695, A257696, A264990, A275729, A275806, A275948, A275964, A278235.
%K A278236 nonn,base
%O A278236 0,2
%A A278236 _Antti Karttunen_, Nov 16 2016

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE