A188629 Numbers k such that k^2 has one more divisor than k^2 - 1.

2, 4, 8, 14, 16, 22, 38, 58, 135, 158, 178, 256, 297, 382, 502, 542, 568, 676, 718, 878, 1202, 1215, 1312, 1318, 1382, 1438, 1593, 1622, 1822, 2018, 2144, 2336, 2558, 2578, 2744, 2858, 2902, 3062, 3118, 3296, 3375, 3778, 3993, 4023, 4064, 4192, 4282

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 06 2011

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000290, A055927, A172438.

Programs

Maple

isA188629 := proc(n) if numtheory[tau](n^2) = numtheory[tau](n^2-1)+1 then true; else false; end if; end proc:
for n from 1 do if isA188629(n) then print(n) ; end if; end do: # R. J. Mathar, Apr 14 2011

Mathematica

Select[Range[10000], DivisorSigma[0, #^2 - 1] + 1 == DivisorSigma[0, #^2] &]

PARI

is(k) = k > 1 && numdiv(k^2-1) + 1 == numdiv(k^2); \\ Amiram Eldar, Apr 17 2024