A055927 Numbers k such that k + 1 has one more divisor than k.

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

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.

Cf. A000005, A006073, A045983, A049820, A075044.

Sequence in context: A209980 A085046 A138495 * A316261 A354958 A249734

Adjacent sequences: A055924 A055925 A055926 * A055928 A055929 A055930

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