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A278965 Numbers k such that k! = 2^a * 3^b * c, where a and b are 0 or powers of 2 and c is relatively prime to 6. 0
1, 2, 3, 6, 7, 10, 11, 18, 19 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Shevelev proves that this sequence contains no other members. Jan-Christoph Schlage-Puchta proves that "a and b are 0 or powers of 2" can be generalized to "a is 0 or a power of 2 and b is 0 or 3-smooth" without changing the sequence.

LINKS

Table of n, a(n) for n=1..9.

Jan-Christoph Schlage-Puchta, The exponents in the prime decomposition of factorials, Archiv der Mathematik 107:6 (2016), pp. 603-608.

V. Shevelev, Compact integers and factorials, Acta Arithmetica 126 (2007), pp. 195-236.

EXAMPLE

11! = 2^8 * 3^4 * 5^2 * 7 * 11 and 8 and 4 are powers of 2, so 11 is in this sequence.

MAPLE

filter:= proc(n)

  local a;

  a:= padic:-ordp(n!, 2);

  if a > 0 and a <> 2^padic:-ordp(a, 2) then return false fi;

  a:= padic:-ordp(n!, 3);

  a = 0 or a = 2^padic:-ordp(a, 2)

end proc:

select(filter, [$1..20]); # Robert Israel, Dec 05 2016

CROSSREFS

Sequence in context: A117206 A026443 A204323 * A032858 A181498 A030703

Adjacent sequences:  A278962 A278963 A278964 * A278966 A278967 A278968

KEYWORD

nonn,fini,full

AUTHOR

Charles R Greathouse IV, Dec 02 2016

STATUS

approved

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Last modified November 13 12:45 EST 2019. Contains 329094 sequences. (Running on oeis4.)