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 A323379 #21 Sep 28 2021 17:33:23 %S A323379 165,315,357,405,495,525,555,567,585,627,675,693,765,795,825,855,891, %T A323379 915,945,957,975,1005,1053,1071,1125,1155,1173,1305,1323,1365,1395, %U A323379 1425,1485,1515,1575,1617,1677,1683,1725,1755,1785,1815,1827,1845,1911,1965,1995 %N A323379 Odd k such that d(k-1) < d(k) and d(k) > d(k+1), d = A000005. %C A323379 Numbers k such that k is in A138171 and that k-1 is in A138172. %C A323379 It's often the case that an odd number has fewer divisors than at least one of its adjacent even numbers. This sequence lists the exceptions. %C A323379 Most terms are congruent to 3 modulo 6. The smallest term congruent to 1 modulo 6 is 2275, and the smallest term congruent to 5 modulo 6 is 6125. %H A323379 Amiram Eldar, <a href="/A323379/b323379.txt">Table of n, a(n) for n = 1..10000</a> %e A323379 d(314) = 4, d(315) = 12, d(316) = 6, so 315 is a term. %p A323379 q:= k-> k::odd and (d-> d(k-1)<d(k) and d(k)>d(k+1))(numtheory[tau]): %p A323379 select(q, [$1..2000])[]; # _Alois P. Heinz_, Sep 28 2021 %t A323379 Select[Range[3, 2001, 2], (d = DivisorSigma[0, #] & /@ (# + Range[-1,1]))[[2]] > d[[1]] && d[[2]] > d[[3]] &] (* _Amiram Eldar_, Jul 22 2019 *) %o A323379 (PARI) forstep(n=3,2000,2,if(numdiv(n)>numdiv(n-1)&&numdiv(n)>numdiv(n+1), print1(n, ", "))) %Y A323379 Intersection of A075027 and A005408. %Y A323379 Cf. A000005, A138171, A138172. %Y A323379 Similar sequences: A076773, A323380. %K A323379 nonn %O A323379 1,1 %A A323379 _Jianing Song_, Jan 12 2019