OFFSET
1,1
COMMENTS
Numbers which can be expressed as a sum of a set of positive consecutive even numbers: Sum_{i=m..m+k} A005843(i), m>=1, k>=1.
Differs from A054741, which contains 105 for example.
These are the numbers that are not free of odd prime factors, but are not odd. Compare with A051144, nonsquarefree nonsquares. The self-inverse function defined by A225546 maps the members of either set 1:1 onto the other set. - Peter Munn, Jul 31 2020 with edit Feb 14 2022
From Charles Kusniec, Jan 06 2026: (Start)
Equivalently, even composite numbers that are not powers of 2.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..20000
FORMULA
a(n) = 2 * A057716(n).
EXAMPLE
6=2+4. 10=4+6. 12=2+4+6. 14=6+8. 18=4+6+8. 20=2+4+6+8. 22=10+12. 24=6+8+10.
MATHEMATICA
z=200; lst={}; Do[c=a; Do[c+=b; If[c<=2*z, AppendTo[lst, c]], {b, a-2, 1, -2}], {a, 2, z, 2}]; Union@lst
PROG
(PARI) isA177712(n) = (!(n%2)&&(0<#select(x -> x%2, factor(n)[, 1]))); \\ Antti Karttunen, Jul 31 2020
(PARI) isA177712(n) = (!(n%2)&&bitand(n, n-1)); \\ Antti Karttunen, Jul 31 2020
(Python)
def A177712(n): return n+(m:=n.bit_length())+(n>=(1<<m)-m)<<1 # Chai Wah Wu, Jun 30 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, May 11 2010
EXTENSIONS
Definition moved into a comment by R. J. Mathar, Aug 15 2010
New name from Peter Munn, Jul 31 2020
New name from Sean A. Irvine, Jan 12 2026
STATUS
approved
