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A075025
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Numbers n such that d(n) < d(n-1) and d(n) < d(n+1), where d(k) is the number of divisors of k.
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3
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5, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 51, 53, 55, 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 89, 91, 97, 101, 103, 107, 109, 111, 113, 115, 121, 125, 127, 129, 131, 137, 139, 149, 151, 153, 155, 157, 161, 163, 167, 169, 173, 175, 179, 181, 183
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| All primes > 3 are members.
Is this sequence of positive density? I expect a(n) ~ 4n but can only prove n (log log n)^k/ log n << a(n) << n for arbitrary k. [Charles R Greathouse IV, May 01 2011]
Number of terms < 10^k: 3, 32, 324, 3222, 32026, 318583, 3181133, 31766404, ..., . - Robert G. Wilson v, May 01 2011.
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EXAMPLE
| 17 is in the sequence because d(16) = 5, d(17) = 2, d(18) = 6 and 5 > 2 < 6.
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MATHEMATICA
| fQ[n_] := DivisorSigma[0, n - 1] > DivisorSigma[0, n] < DivisorSigma[0, n + 1]; Select[ Range@ 200, fQ] (* Robert G. Wilson v, May 01 2011 *)
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CROSSREFS
| Cf. A075026, A075027.
Sequence in context: A065155 A088502 A081001 * A075394 A158439 A124112
Adjacent sequences: A075022 A075023 A075024 * A075026 A075027 A075028
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 02 2002
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EXTENSIONS
| Corrected and extended by Jason Earls (zevi_35711(AT)yahoo.com), Sep 04 2002
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