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A067807
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Numbers n such that sigma(n)^2 > 2*sigma(n^2).
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2
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24, 36, 40, 48, 60, 72, 80, 84, 90, 96, 108, 112, 120, 126, 132, 140, 144, 156, 160, 168, 176, 180, 192, 200, 204, 208, 210, 216, 224, 228, 240, 252, 264, 270, 276, 280, 288, 300, 312, 320, 324, 336, 348, 352, 360, 372, 378, 384, 392, 396, 400, 408, 416, 420
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OFFSET
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1,1
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COMMENTS
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For every n>1 sigma(n)^2 > sigma(n^2).
Lim_{n->inf} a(n)/n appears to exist and is near 8.0; e.g., a(124094) = 1000000. - Paul D. Hanna, Sep 22 2011
We also have a(12438441) = 10^8, a(124240921) = 10^9, and a(1242729194) = 10^10. - Giovanni Resta, Jun 15 2018
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LINKS
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EXAMPLE
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The limit a(n)/n seems to be near 8.0:
n a(n) a(n)/n
------- -------- ----------
124094 1000000 8.05840...
248310 2000000 8.05444...
372503 3000000 8.05362...
496826 4000000 8.05110...
621163 5000000 8.04941...
745602 6000000 8.04718...
870189 7000000 8.04422...
994799 8000000 8.04182...
1119336 9000000 8.04048...
1243884 10000000 8.03933...
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MATHEMATICA
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Select[Range[500], DivisorSigma[1, #]^2>2DivisorSigma[1, #^2]&] (* Harvey P. Dale, Mar 30 2011 *)
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PROG
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(PARI) {for(n=1, 8000, if(2*sigma(n^2)-sigma(n)^2 < 0, print1(n, ", ")))} \\ Paul D. Hanna, Sep 22 2011
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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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