A323380 -id:A323380 - cp's OEIS frontend

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

Jianing Song, Jan 12 2019

nonn

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.

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

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

Intersection of A075027 and A005408.
Cf. A000005, A138171, A138172.
Similar sequences: A076773, A323380.

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

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

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

A323726 Odd numbers k such that sigma(k-1) < sigma(k) < sigma(k+1), sigma(n) = A000203.

Original entry on oeis.org

3, 63, 75, 135, 147, 195, 255, 399, 459, 483, 495, 555, 567, 615, 627, 663, 675, 735, 759, 795, 819, 855, 915, 975, 999, 1035, 1095, 1215, 1239, 1287, 1323, 1455, 1515, 1539, 1647, 1659, 1683, 1815, 1827, 1875, 1935, 2079, 2115, 2175, 2235, 2247, 2295, 2415, 2499

Offset: 1

K. D. Bajpai, Nov 19 2019

nonn

It appears that most of the terms are divisible by 3; the smallest exception is 13475.

Up to 10^9, 223182 of 20606497 (about 1%) of the terms are not divisible by 3. - Charles R Greathouse IV, Nov 28 2019

			sigma(62) = 96, sigma(63) = 104, sigma(64) = 127. Hence, 63 is in the sequence.
sigma(74) = 114, sigma(75) = 124, sigma(76) = 140. Hence, 75 is in the sequence.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000203, A005408, A053224, A067828, A323380.

f:=func; [k:k in [3..2500 by 2]| f(k-1) and f(k)] // Marius A. Burtea, Nov 19 2019

Sigmas:= map(numtheory:-sigma, [$1..3000]):
select(t -> Sigmas[t-1] < Sigmas[t] and Sigmas[t] < Sigmas[t+1],
[seq(i,i=3..3000,2)]); # Robert Israel, Nov 23 2019

Select[Range[1,8000,2], DivisorSigma[1, # - 1] < DivisorSigma[1, (#)] && DivisorSigma[1, #] < DivisorSigma[1, (# + 1)] &]

cp's OEIS Frontend

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

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