A075044 -id:A075044 - cp's OEIS frontend

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

Labos Elemer, Jul 21 2000

nonn

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

			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.

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1000 terms from Donovan Johnson)

Numbers where repetition occurs in A049820.

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

Select[ Range[ 200000], DivisorSigma[0, # ] + 1 == DivisorSigma[0, # + 1] &]
Position[Differences[DivisorSigma[0,Range[170000]]],1]//Flatten (* Harvey P. Dale, Jul 06 2025 *)

for(n=1,1000,if(numdiv(n+1)-numdiv(n)==1,print1(n,", "))); /* Joerg Arndt, Apr 09 2011 */

More terms from David W. Wilson, Sep 06 2000, who remarks that every element is of form n^2 or n^2 - 1.

A075046 a(n) = the smallest number k such that the number of divisors of the n numbers from k through k+n-1 are in nondescending order.

Original entry on oeis.org

1, 1, 1, 1, 241, 241, 12853, 12853, 234613, 376741, 78312721, 125938261, 4019167441, 16586155153, 35237422882, 1296230533473, 42301168491121, 61118966262061

Offset: 1

Amarnath Murthy, Sep 03 2002

tau(k) <= tau(k+1) <= ... <= tau(k+n-1).
a(16) > 10^12. - Donovan Johnson, Oct 13 2009
a(17) > 10^13. - Giovanni Resta, Apr 12 2017
a(19) > 2.64*10^15. - Jud McCranie, Mar 27 2019
If a(n) > 1, then A013632(a(n)) >= n. Might be useful to help speed up brute force search. - Chai Wah Wu, May 04 2017

			a(5) = 241 = a(6) as tau(241) = 2 < tau(242) = tau(243) = tau(244) = tau(245) = 6 < tau(246).

Cf. A075028, A075029, A075031, A045983, A006073, A075044, A055927, A075047.

k = 1; Do[ While[t = Table[ DivisorSigma[0, i], {i, k, k + n - 1}]; t != Sort[t], k++ ]; Print[k], {n, 1, 11}]

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003
a(11) from Robert G. Wilson v, Sep 07 2003
a(12)-a(15) from Donovan Johnson, Oct 13 2009
a(16) from Fred Schneider, Mar 29 2017
a(17)-a(18) from Jud McCranie, Mar 27 2019

cp's OEIS Frontend

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

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