A046791 - OEIS

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.

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: A374840 A239641 A249151 * A187203 A187202 A345046

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