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Search: id:A164119
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| A164119 |
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Numbers n that are the smallest number that produces the ordered pair (d(n),d(n+1)), where d(n) is the number of divisors of n. |
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+0
1
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| 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 15, 16, 20, 23, 24, 27, 30, 35, 36, 39, 44, 47, 48, 49, 54, 59, 60, 63, 64, 80, 81, 84, 95, 99, 104, 111, 112, 119, 120, 143, 144, 152, 153, 167, 169, 175, 176, 179, 180, 191, 192, 195, 210, 216, 224, 225, 239, 240, 252, 260, 272, 275
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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It appears that the set of numbers that produces a given ordered pair (i,j) is either empty, finite, or infinite. The pair (3,3) is produced by no number because d(n)=3 only if n is a positive square and there are no consecutive positive squares. Sequence A161460 lists n that produce a unique ordered pair. It appears that the ordered pair (4,2) is produced by an infinite number of n, which is another way of conjecturing that there are an infinite number of safe primes, A005385. The pair (2,4) is produced by primes in A005383. The numbers in A039832 produce the pair (4,4).
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LINKS
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T. D. Noe, Terms less than 10^9
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EXAMPLE
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7 is not here because (d(7),d(8)) = (2,4), which is the same ordered pair produced by n=5.
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MATHEMATICA
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s={}; Reap[Do[pr=DivisorSigma[0, {n, n+1}]; If[ !MemberQ[s, pr], AppendTo[s, pr]; Sow[n]], {n, 1000}]][[2, 1]]
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CROSSREFS
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Sequence in context: A052047 A078831 A031177 this_sequence A033102 A030749 A030789
Adjacent sequences: A164116 A164117 A164118 this_sequence A164120 A164121 A164122
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Aug 10 2009
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