A373903 Numbers k such that k^2 - 1 has fewer divisors than k^2 + 1.

18, 72, 132, 138, 182, 192, 228, 242, 268, 278, 282, 327, 348, 360, 378, 382, 408, 418, 432, 438, 618, 632, 642, 660, 682, 684, 693, 718, 772, 788, 798, 822, 843, 858, 882, 918, 948, 957, 1032, 1048, 1068, 1092, 1113, 1118, 1143, 1152, 1227, 1228, 1230, 1282, 1292

Offset: 1

Author

Amiram Eldar, Jun 22 2024

Keywords

• nonn
• easy

Comments

Numbers k such that A347191(k) < A193432(k).

Examples

			18 is a term since 18^2 - 1 = 323 has 4 divisors (1, 17, 19 and 323) while 18^2 + 1 = 325 has 6 divisors (1, 5, 13, 25, 65 and 325).
		

Links

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

Crossrefs

Cf. A000005, A002522, A005563, A069062, A188629, A193432, A347191.

Programs

Mathematica

Select[Range[2, 1300], DivisorSigma[0, #^2 - 1] < DivisorSigma[0, #^2 + 1] &]

PARI

is(k) = k > 1 && numdiv(k^2 - 1) < numdiv(k^2 + 1);