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A046791
A046790 has several definitions, one of which is: "Numbers i such that there is a smaller positive number j such that (i+j)/2 and sqrt(i*j) are integers". The present sequence gives the smallest choice for j.
3
2, 1, 4, 2, 6, 1, 3, 2, 4, 10, 5, 12, 1, 2, 6, 14, 7, 4, 2, 3, 20, 1, 22, 10, 6, 2, 11, 4, 26, 12, 28, 13, 30, 1, 5, 14, 2, 15, 34, 4, 3, 6, 38, 17, 10, 2, 42, 1, 19, 7, 44, 20, 46, 21, 12, 4, 22, 2, 23, 52, 6, 14, 1, 58, 26, 60, 2, 3, 5, 62, 10, 28, 4, 29, 66, 30, 68, 11, 31, 70, 2, 1, 6, 74, 33
OFFSET
1,1
COMMENTS
Note that A046790 is the complement of A078779. - Omar E. Pol, Jun 11 2016
LINKS
FORMULA
Let b(n)=A046790(n). Let k=k(n) be the greatest number whose square divides b(n) and is such that b(n) and b(n)/k^2 are of the same parity. Then a(n) = b(n)/k^2. - Vladimir Shevelev, Jun 07 2016
Or, equivalently, a(n) is the squarefree part s(n) of b(n), if either b(n) is odd or s(n) is even. Otherwise, when b(n) is even, but s(n) is odd, a(n)=4*s(n). - David A. Corneth, Jun 07 2016
EXAMPLE
From Vladimir Shevelev, Jun 07 2016: (Start)
A046790(5)=24 with even squarefree part (6), so a(5) = 6;
A046790(12)=48 with odd squarefree part (3), so a(12) = 3*4=12.
(End)
PROG
(PARI) a(n) = my(n=A046790(n), f=factor(n), p=n%2); f[, 2]=f[, 2]%2; r=prod(i=1, matsize(f)[1], f[i, 1]^f[i, 2]); r*=(4^(n%2==0&&r%2==1)) \\ David A. Corneth, Jun 07 2016
CROSSREFS
Cf. A046790.
Sequence in context: A374840 A239641 A249151 * A187203 A187202 A345046
KEYWORD
nonn
AUTHOR
David W. Wilson, Dec 11 1999
EXTENSIONS
Entry revised by N. J. A. Sloane, with help from Don Reble and several OEIS editors. Jun 07 2016
STATUS
approved