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A225756
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Runs of consecutive numbers with the same number of divisors.
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3
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2, 3, 14, 15, 21, 22, 26, 27, 33, 34, 35, 38, 39, 44, 45, 57, 58, 75, 76, 85, 86, 87, 93, 94, 95, 98, 99, 104, 105, 116, 117, 118, 119, 122, 123, 133, 134, 135, 136, 141, 142, 143, 145, 146, 147, 148, 158, 159, 171, 172, 177, 178, 189, 190, 201, 202, 203
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listen;
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OFFSET
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1,1
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COMMENTS
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The first run of length 3 is {33,34,35}; the first of length 4: {116, 117, 118, 119}; of length 5: {2641, 2642, 2643, 2644, 2645}; of length 6: {1081, 1082, 1083, 1084, 1085, 1086}; of length 7: {25781, 25782, 25783, 25784, 25785, 25786, 25787}; of length 8: {77673, 77674, 77675, 77676, 77677, 77678, 77679, 77680}.
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LINKS
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EXAMPLE
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Sequence begins:
2, 3;
14, 15;
21, 22;
26, 27;
33, 34, 35;
38, 39;
etc.
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MATHEMATICA
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sel = Select[Range[300], DivisorSigma[0, #] == DivisorSigma[0, # + 1] &]; Union[sel, sel + 1]
Flatten[SequencePosition[DivisorSigma[0, Range[300]], {x_, x_}]]//Union (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 22 2021 *)
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CROSSREFS
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Cf. A225757 (same sum of divisors).
Cf. A225758 (same number and sum of divisors).
Cf. A140578 (first term of every run).
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KEYWORD
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nonn,easy,tabf
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AUTHOR
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STATUS
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approved
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