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Search: id:A055927
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| A055927 |
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Smallest number k such that k and k+1 have n and n+1 divisors. |
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+0
2
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| 1, 3, 9, 15, 25, 63, 121, 195, 255, 361, 483, 729, 841, 1443, 3363, 3481, 3721, 5041, 6241, 10201, 15625, 17161, 18224, 19321, 24963, 31683, 32761, 39601, 58564, 59049, 65535, 73441, 88208, 110889, 121801, 143641, 145923, 149769, 167281
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OFFSET
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1,2
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COMMENT
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This means that n+1-d(n+1)=n-d(n), i.e. d(n+1)-d(n)=1, where d() is A000005, the number of divisors.
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EXAMPLE
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a(4) = 15 as 15 has 4 and 16 has 5 divisors. a(6) = 63 as 63 and 64 have 6 and 7 divisors respectively.
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MATHEMATICA
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Select[ Range[ 200000], DivisorSigma[0, # ] + 1 == DivisorSigma[0, # + 1] &]
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CROSSREFS
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Numbers where repetition occurs in A049820.
Cf. A000005, A049820, A075041, A045983, A006073, A075044.
Sequence in context: A099989 A085046 A138495 this_sequence A087031 A089632 A082897
Adjacent sequences: A055924 A055925 A055926 this_sequence A055928 A055929 A055930
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jul 21 2000
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EXTENSIONS
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More terms from David W. Wilson (davidwwilson(AT)comcast.net), Sep 06 2000, who remarks that every element is of form n^2 or n^2-1.
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