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A046791
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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.
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3
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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
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1,1
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COMMENTS
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LINKS
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FORMULA
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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
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EXAMPLE
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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)
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PROG
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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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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