

A323379


Odd k such that d(k1) < 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
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OFFSET

1,1


COMMENTS

Numbers k such that k is in A138171 and that k1 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(k1)<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(n1)&&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



