A373903 - OEIS

%I #11 Jun 22 2024 08:02:39

%S 18,72,132,138,182,192,228,242,268,278,282,327,348,360,378,382,408,

%T 418,432,438,618,632,642,660,682,684,693,718,772,788,798,822,843,858,

%U 882,918,948,957,1032,1048,1068,1092,1113,1118,1143,1152,1227,1228,1230,1282,1292

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

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

%H Amiram Eldar, <a href="/A373903/b373903.txt">Table of n, a(n) for n = 1..10000</a>

%e 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).

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

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

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

%K nonn,easy

%O 1,1

%A _Amiram Eldar_, Jun 22 2024