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A323379 Odd k such that d(k-1) < d(k) and d(k) > d(k+1), d = A000005. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

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

EXAMPLE

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

MAPLE

q:= k-> k::odd and (d-> d(k-1)<d(k) and d(k)>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 *)

PROG

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

CROSSREFS

Intersection of A075027 and A005408.

Cf. A000005, A138171, A138172.

Similar sequences: A076773, A323380.

Sequence in context: A319328 A301970 A176877 * A215967 A029563 A145665

Adjacent sequences:  A323376 A323377 A323378 * A323380 A323381 A323382

KEYWORD

nonn

AUTHOR

Jianing Song, Jan 12 2019

STATUS

approved

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Last modified January 26 21:14 EST 2022. Contains 350600 sequences. (Running on oeis4.)