

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




OFFSET

1,2


COMMENTS

Shevelev proves that this sequence contains no other members. JanChristoph SchlagePuchta 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 3smooth" without changing the sequence.


LINKS

Table of n, a(n) for n=1..9.
JanChristoph SchlagePuchta, The exponents in the prime decomposition of factorials, Archiv der Mathematik 107:6 (2016), pp. 603608.
V. Shevelev, Compact integers and factorials, Acta Arithmetica 126 (2007), pp. 195236.


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



