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A338790
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a(n) = rad(n)^2 - sigma(n), where rad(n) is the squarefree kernel of n (A007947) and sigma(n) is the sum of divisors of n (A000203).
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2
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0, 1, 5, -3, 19, 24, 41, -11, -4, 82, 109, 8, 155, 172, 201, -27, 271, -3, 341, 58, 409, 448, 505, -24, -6, 634, -31, 140, 811, 828, 929, -59, 1041, 1102, 1177, -55, 1331, 1384, 1465, 10, 1639, 1668, 1805, 400, 147, 2044, 2161, -88, -8, 7, 2529, 578, 2755, -84, 2953
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OFFSET
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1,3
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COMMENTS
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It is conjectured that only 1 and 1782 satisfy a(x) = 0.
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REFERENCES
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R. K. Guy, Unsolved Problems in Theory of Numbers, Springer-Verlag, Third Edition, 2004, B11.
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LINKS
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Yong-Gao Chen, and Xin Tong, On a conjecture of de Koninck, Journal of Number Theory, Volume 154, September 2015, Pages 324-364. Beware of typo 1728.
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FORMULA
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MAPLE
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a:= n-> mul(i[1], i=ifactors(n)[2])^2-numtheory[sigma](n):
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PROG
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(PARI) a(n) = my(f=factor(n)); factorback(f[, 1])^2 - sigma(f);
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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