This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A339863 #21 Aug 14 2024 16:54:29 %S A339863 187,243,403,423,425,427,435,583,663,729,763,775,845,891,1003,1083, %T A339863 1125,1265,1267,1375,1395,1419,1545,1573,1575,1615,1643,1645,1755, %U A339863 1771,1813,1843,1885,1925,1953,2035,2275,2385,2403,2523,2525,2533,2635,2673,2695 %N A339863 Odd numbers k > 1 such that A005179(k-1) > A005179(k) < A005179(k+1) > A005179(k+2) < A005179(k+3). %C A339863 Odd numbers k such that k and k+2 are both in A328897. %C A339863 Despite the fact that only square numbers have an odd number of divisors, there are surprisingly many terms here. The numbers of terms below 10^3, 10^4 and 10^5 are 14, 208 and 3004 respectively. %H A339863 Matthew House, <a href="/A339863/b339863.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..3004 below 10^5 from Jianing Song) %e A339863 The smallest numbers with exactly 582, 583, 584, 585 and 586 divisors are ~3.565*10^30, ~2.659*10^20, ~4.958*10^24, 406425600 and ~2.387*10^88 respectively. We have A005179(582) > A005179(583) < A005179(584) > A005179(585) < A005179(586), hence 583 is a term. %o A339863 (PARI) isA339863(k) = if(k%2&&k>1, my(v=vector(5, n, A005179(k-2+n))); v[2]<v[1] && v[2]<v[3] && v[4]<v[3] && v[4]<v[5], 0) %Y A339863 Cf. A005179, A328897. %K A339863 nonn %O A339863 1,1 %A A339863 _Jianing Song_, Dec 19 2020