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A055927
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Numbers k such that k + 1 has one more divisor than k.
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10
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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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COMMENTS
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Numbers k such that d(k+1) - d(k) = 1, where d(k) is A000005(k), the number of divisors.
Numbers k such that A049820(k) = A049820(k+1). - Jaroslav Krizek, Feb 10 2014
Numbers k such that A051950(k+1) = 1. - Danny Rorabaugh, Oct 05 2017
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LINKS
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Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1000 terms from Donovan Johnson)
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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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MAPLE
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select(n->tau(n+1)=tau(n)+1, [$1..2*10^5]); # Paolo P. Lava, Aug 02 2018
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MATHEMATICA
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Select[ Range[ 200000], DivisorSigma[0, # ] + 1 == DivisorSigma[0, # + 1] &]
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PROG
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(PARI) for(n=1, 1000, if(numdiv(n+1)-numdiv(n)==1, print1(n, ", "))); /* Joerg Arndt, Apr 09 2011 */
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CROSSREFS
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Numbers where repetition occurs in A049820.
Cf. A000005, A006073, A045983, A049820, A075044.
Sequence in context: A209980 A085046 A138495 * A316261 A249734 A319316
Adjacent sequences: A055924 A055925 A055926 * A055928 A055929 A055930
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KEYWORD
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nonn
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AUTHOR
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Labos Elemer, Jul 21 2000
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EXTENSIONS
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More terms from David W. Wilson, Sep 06 2000, who remarks that every element is of form n^2 or n^2 - 1.
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STATUS
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approved
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