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

%I A055927 #43 Jul 06 2025 12:41:12
%S A055927 1,3,9,15,25,63,121,195,255,361,483,729,841,1443,3363,3481,3721,5041,
%T A055927 6241,10201,15625,17161,18224,19321,24963,31683,32761,39601,58564,
%U A055927 59049,65535,73441,88208,110889,121801,143641,145923,149769,167281
%N A055927 Numbers k such that k + 1 has one more divisor than k.
%C A055927 Numbers k such that d(k+1) - d(k) = 1, where d(k) is A000005(k), the number of divisors.
%C A055927 Numbers k such that A049820(k) = A049820(k+1). - _Jaroslav Krizek_, Feb 10 2014
%C A055927 Numbers k such that A051950(k+1) = 1. - _Danny Rorabaugh_, Oct 05 2017
%H A055927 Giovanni Resta, <a href="/A055927/b055927.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Donovan Johnson)
%e A055927 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.
%t A055927 Select[ Range[ 200000], DivisorSigma[0, # ] + 1 == DivisorSigma[0, # + 1] &]
%t A055927 Position[Differences[DivisorSigma[0,Range[170000]]],1]//Flatten (* _Harvey P. Dale_, Jul 06 2025 *)
%o A055927 (PARI) for(n=1,1000,if(numdiv(n+1)-numdiv(n)==1,print1(n,", "))); /* _Joerg Arndt_, Apr 09 2011 */
%Y A055927 Numbers where repetition occurs in A049820.
%Y A055927 Cf. A000005, A006073, A045983, A049820, A075044.
%K A055927 nonn
%O A055927 1,2
%A A055927 _Labos Elemer_, Jul 21 2000
%E A055927 More terms from _David W. Wilson_, Sep 06 2000, who remarks that every element is of form n^2 or n^2 - 1.