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%I #21 Sep 28 2021 17:33:23
%S 165,315,357,405,495,525,555,567,585,627,675,693,765,795,825,855,891,
%T 915,945,957,975,1005,1053,1071,1125,1155,1173,1305,1323,1365,1395,
%U 1425,1485,1515,1575,1617,1677,1683,1725,1755,1785,1815,1827,1845,1911,1965,1995
%N Odd k such that d(k-1) < d(k) and d(k) > d(k+1), d = A000005.
%C Numbers k such that k is in A138171 and that k-1 is in A138172.
%C 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 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 Amiram Eldar, <a href="/A323379/b323379.txt">Table of n, a(n) for n = 1..10000</a>
%e d(314) = 4, d(315) = 12, d(316) = 6, so 315 is a term.
%p q:= k-> k::odd and (d-> d(k-1)<d(k) and d(k)>d(k+1))(numtheory[tau]):
%p select(q, [$1..2000])[]; # _Alois P. Heinz_, Sep 28 2021
%t Select[Range[3, 2001, 2], (d = DivisorSigma[0, #] & /@ (# + Range[-1,1]))[[2]] > d[[1]] && d[[2]] > d[[3]] &] (* _Amiram Eldar_, Jul 22 2019 *)
%o (PARI) forstep(n=3,2000,2,if(numdiv(n)>numdiv(n-1)&&numdiv(n)>numdiv(n+1), print1(n, ", ")))
%Y Intersection of A075027 and A005408.
%Y Cf. A000005, A138171, A138172.
%Y Similar sequences: A076773, A323380.
%K nonn
%O 1,1
%A _Jianing Song_, Jan 12 2019
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