The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A251725

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A251725

Smallest number b such that in base-b representation the prime factors of n have equal lengths.
(history; published version)

#16 by Joerg Arndt at Sun Jun 30 10:16:14 EDT 2019

STATUS

proposed

approved

#15 by Jon E. Schoenfield at Sun Jun 30 09:27:36 EDT 2019

STATUS

editing

proposed

#14 by Jon E. Schoenfield at Sun Jun 30 09:27:33 EDT 2019

NAME

Smallest number b such that in base -b representation the prime factors of n have equal lengths.

STATUS

approved

editing

#13 by N. J. A. Sloane at Thu Dec 18 02:06:12 EST 2014

STATUS

proposed

approved

#12 by Jon E. Schoenfield at Thu Dec 18 00:14:59 EST 2014

STATUS

editing

proposed

#11 by Jon E. Schoenfield at Thu Dec 18 00:14:56 EST 2014

COMMENTS

The "base-1" is here same as "unary base", where n is represented with digit "1" duplicated replicated n times. Thus if and only if n is in A000961 (is a power of prime), a(n) = 1. See A252375 for a more consistent treating treatment of those cases.

FORMULA

a(n) = a(A066048(n)). [The result depends only on the smallest and the largest prime factor of n].]

STATUS

proposed

editing

#10 by Antti Karttunen at Wed Dec 17 15:13:12 EST 2014

STATUS

editing

proposed

#9 by Antti Karttunen at Wed Dec 17 15:01:08 EST 2014

FORMULA

a(n) = a(A066048(n)). [The result depends only on the smallest and the largest prime factor of n].

CROSSREFS

Cf. A001358, A006530, A020639, A066048, A138510, A162319.

Cf. A027748.

#8 by Reinhard Zumkeller at Wed Dec 17 11:50:07 EST 2014

PROG

(Haskell)

import Data.List (unfoldr); import Data.Tuple (swap)

a251725 1 = 1

a251725 n = if length ps == 1 then 1 else head $ filter f [2..] where

f b = all (== len) lbs where len:lbs = map (length . d b) ps

ps = a027748_row n

d b = unfoldr (\z -> if z == 0 then Nothing else Just $ swap $ divMod z b)

-- Reinhard Zumkeller, Dec 17 2014

CROSSREFS

Cf. A027748.

#7 by Antti Karttunen at Wed Dec 17 10:43:58 EST 2014

COMMENTS

The "base-1" is here same as "unary base", where n is represented with digit "1" duplicated n times. Thus if and only if n is in A000961 (is a power of prime), a(n) = 1. See A252375 for a more consistent variant treating of this sequencethose cases.