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A015713
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Numbers m such that phi(m) * sigma(m) + k^2 is not a square for any k.
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2
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4, 9, 18, 49, 81, 98, 121, 162, 242, 361, 529, 722, 729, 961, 1058, 1458, 1849, 1922, 2209, 2401, 3481, 3698, 4418, 4489, 4802, 5041, 6241, 6561, 6889, 6962, 8978, 10082, 10609, 11449, 12482, 13122, 13778, 14641, 16129, 17161
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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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Conjecture: {4, p^(2*m), 2*p^(2*m), p = 4*k+3 is prime}. - Sean A. Irvine, Dec 06 2018
The conjecture is true. It can be proved using the multiplicative property of A062354(n), i.e., A062354(p^e) = p^(e-1)*(p^(e+1)-1), and that if m is a term then A007814(A062354(m)) = 1. - Amiram Eldar, Feb 11 2024
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MATHEMATICA
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nonSqDiffQ[n_] := Mod[n, 4] == 2; aQ[n_] := nonSqDiffQ[ EulerPhi[n] * DivisorSigma[ 1, n]]; Select[Range[20000], aQ] (* Amiram Eldar, Dec 07 2018 *)
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PROG
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(PARI) isok(n) = (sigma(n)*eulerphi(n) % 4) == 2; \\ Michel Marcus, Dec 07 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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