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A230653
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Numbers k such that tau(k+1) - tau(k) = 3, where tau(k) = the number of divisors of k (A000005).
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6
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49, 99, 1023, 1681, 1935, 2499, 8649, 9603, 20449, 21903, 23715, 29583, 30975, 38024, 43263, 58563, 60515, 71824, 74528, 110223, 130321, 136899, 145924, 150543, 154449, 165649, 181475, 216224, 224675, 233288, 243049, 256035, 258063, 265225, 294849, 300303
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OFFSET
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1,1
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COMMENTS
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Numbers k such that A051950(k+1) = 3.
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LINKS
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EXAMPLE
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99 is in the sequence because tau(100) - tau(99) = 9 - 6 = 3.
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MATHEMATICA
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Select[ Range[ 50000], DivisorSigma[0, # ] + 3 == DivisorSigma[0, # + 1] &]
Position[Differences[DivisorSigma[0, Range[300400]]], 3]//Flatten (* Harvey P. Dale, Jun 30 2022 *)
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PROG
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(PARI) isok(n) = numdiv(n+1) - numdiv(n) == 3; \\ Michel Marcus, Oct 27 2013
(Python)
from sympy import divisor_count as tau
from itertools import count, islice
for m in count(1):
mm = m*m
tmm = tau(mm)
if tmm - tau(mm-1) == 3: yield mm-1
if tau(mm+1) - tmm == 3: yield mm
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CROSSREFS
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Cf. A055927 (numbers n such that tau(n+1) - tau(n) = 1), A230115 (numbers n such that tau(n+1) - tau(n) = 2), A000005.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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