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A067356
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Numbers k such that prime(k+3)-(k+3)*tau(k+3) = prime(k)-k*tau(k) where tau(k) = A000005(k) is the number of divisors of k.
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5
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172, 206, 435, 542, 551, 575, 611, 626, 718, 759, 903, 955, 1102, 1238, 1495, 1711, 2009, 2379, 2385, 2482, 2572, 2815, 2874, 3018, 3103, 3222, 3225, 3802, 3899, 4055, 4335, 4342, 4430, 4439, 4545, 4682, 5154, 5183, 5467, 5594, 6036, 6058, 6202, 6231
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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ptQ[n_]:=Module[{n3=n+3}, Prime[n3]-(n3)DivisorSigma[0, n3]==Prime[n]- n*DivisorSigma[ 0, n]]; Select[Range[6300], ptQ] (* Harvey P. Dale, Jul 22 2012 *)
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PROG
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(PARI) f(n) = prime(n) - n * numdiv(n);
is(n) = n > 3 && f(n) == f(n+3); \\ Amiram Eldar, Apr 08 2024
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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