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A260651 Number of factorions in base n. 0
2, 2, 3, 3, 4, 2, 2, 3, 4, 5, 2, 3, 3, 4, 3, 5, 2, 2, 2, 3, 2, 3, 4, 2, 4, 4, 3, 2, 3, 2, 4, 2, 6, 3, 3, 3, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

1 and 2 are factorions of every integer number base, since 1 = 1! and 2 = 2!. Thus every integer number base has at least 2 factorions. - Michael De Vlieger, Nov 23 2015

A factorion is an integer which is equal to the sum of factorials of its digits. See A193163 for the list of all factorions in base n. - M. F. Hasler, Nov 25 2015

LINKS

Table of n, a(n) for n=2..39.

Eric Weisstein's World of Mathematics, Factorion

EXAMPLE

a(6) = 4 because base 6 has the factorions {1, 2, 25, 26}. Expressed in base 6 these are {1, 2, 41, 42}. 1! = 1 and 2! = 2 and are factorions in every integer base b >= 2. Additionally, 4! + 1! = 24 + 1 = 25 and 4! + 2! = 24 + 2 = 26. - Michael De Vlieger, Nov 23 2015

a(2) = 2 = #{ 1, 2 }, indeed 1 = 1! and 2 = 10[2] = 1! + 0! and there cannot be any other since the sum of factorials of the binary digits equals the number of these digits, and from 3 on all numbers are larger than the number of their binary digits. - M. F. Hasler, Nov 25 2015

MATHEMATICA

Table[Length@ Select[Range[n Factorial[n - 1]], Total@ Map[Factorial, #] &@ IntegerDigits[#, n] == # &], {n, 2, 10}] (* Michael De Vlieger, Nov 23 2015 *)

CROSSREFS

Cf. A014080, A193163.

Sequence in context: A326031 A322997 A085561 * A116370 A261018 A106486

Adjacent sequences:  A260648 A260649 A260650 * A260652 A260653 A260654

KEYWORD

nonn,base,more

AUTHOR

Eric M. Schmidt (based on data from A193163), Nov 16 2015

STATUS

approved

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Last modified September 22 03:54 EDT 2020. Contains 337289 sequences. (Running on oeis4.)