OFFSET
1,1
COMMENTS
Conjectures: 2n > a(n) or 2n < a(n) for infinitely many values of n and abs(a(n)-2n) < sqrt(n) for n > 45. a(n)=2n for n = 318, 338, 350, 488, 490, 492, 494,...
Numbers divisible by 16 which have no prime factors = 1 mod 4, together with numbers not divisible by 16 which have exactly one prime factor = 1 mod 4. This refutes the conjectures. - Charles R Greathouse IV, Apr 16 2012
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
a(n) seems to be asymptotic to 2n.
MATHEMATICA
Select[Range[3, 125], Length[Reduce[x^4 - 1 == 0, x, Modulus -> #]] == 2*Length[Reduce[x^2 - 1 == 0, x, Modulus -> #]] &] (* Jayanta Basu, Jul 01 2013 *)
PROG
(PARI) is(n)=my(v=factor(n)[, 1]%4, s=sum(i=1, #v, v[i]==1), e=valuation(n, 2)); s==(e<4) \\ Charles R Greathouse IV, Apr 16 2012
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Aug 19 2002
STATUS
approved