

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
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OFFSET

1,1


COMMENTS

Note that A046790 is the complement of A078779.  Omar E. Pol, Jun 11 2016


LINKS

David A. Corneth, Table of n, a(n) for n = 1..10000


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: A141564 A239641 A249151 * A187203 A187202 A125131
Adjacent sequences: A046788 A046789 A046790 * A046792 A046793 A046794


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



