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A055927 Numbers k such that k + 1 has one more divisor than k. 14
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1000 terms from Donovan Johnson)
EXAMPLE
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.
MATHEMATICA
Select[ Range[ 200000], DivisorSigma[0, # ] + 1 == DivisorSigma[0, # + 1] &]
PROG
(PARI) for(n=1, 1000, if(numdiv(n+1)-numdiv(n)==1, print1(n, ", "))); /* Joerg Arndt, Apr 09 2011 */
CROSSREFS
Numbers where repetition occurs in A049820.
Sequence in context: A209980 A085046 A138495 * A316261 A354958 A249734
KEYWORD
nonn
AUTHOR
Labos Elemer, Jul 21 2000
EXTENSIONS
More terms from David W. Wilson, Sep 06 2000, who remarks that every element is of form n^2 or n^2 - 1.
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)