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A278234 Filter-sequence for factorial base (digit slopes): Least number with the same prime signature as A275734(n). 7
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
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(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 ...").

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(A275734(n)).

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

PROG

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

CROSSREFS

Cf. A007623, A046523, A225901, A275734.

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

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

Sequence in context: A293443 A247765 A129750 * A068976 A265392 A253139

Adjacent sequences:  A278231 A278232 A278233 * A278235 A278236 A278237

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 16 2016

STATUS

approved

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Last modified April 22 06:14 EDT 2019. Contains 322329 sequences. (Running on oeis4.)