A323379 Odd k such that d(k-1) < d(k) and d(k) > d(k+1), d = A000005.

165, 315, 357, 405, 495, 525, 555, 567, 585, 627, 675, 693, 765, 795, 825, 855, 891, 915, 945, 957, 975, 1005, 1053, 1071, 1125, 1155, 1173, 1305, 1323, 1365, 1395, 1425, 1485, 1515, 1575, 1617, 1677, 1683, 1725, 1755, 1785, 1815, 1827, 1845, 1911, 1965, 1995

Offset: 1

Author

Jianing Song, Jan 12 2019

Keywords

• nonn

Comments

Numbers k such that k is in A138171 and that k-1 is in A138172.

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.

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.

Examples

			d(314) = 4, d(315) = 12, d(316) = 6, so 315 is a term.
		

Links

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

Crossrefs

Intersection of A075027 and A005408.

Cf. A000005, A138171, A138172.

Similar sequences: A076773, A323380.

Programs

Maple

q:= k-> k::odd and (d-> d(k-1)d(k+1))(numtheory[tau]):
select(q, [$1..2000])[];  # Alois P. Heinz, Sep 28 2021

Mathematica

Select[Range[3, 2001, 2], (d = DivisorSigma[0, #] & /@ (# + Range[-1,1]))[[2]] > d[[1]] && d[[2]] > d[[3]] &] (* Amiram Eldar, Jul 22 2019 *)

PARI

forstep(n=3,2000,2,if(numdiv(n)>numdiv(n-1)&&numdiv(n)>numdiv(n+1), print1(n, ", ")))