This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 21 08:53 EDT 2019. Contains 323441 sequences. (Running on oeis4.)