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
Offset: 1
Keywords
Examples
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)
Links
- David A. Corneth, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A046790.
Programs
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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
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
Extensions
Entry revised by N. J. A. Sloane, with help from Don Reble and several OEIS editors. Jun 07 2016
Comments