A067828 -id:A067828 - cp's OEIS frontend

A323380 Odd n such that sigma(n) > sigma(n+1) and sigma(n) > sigma(n-1), sigma = A000203.

315, 405, 525, 693, 765, 945, 1125, 1155, 1395, 1575, 1755, 1785, 1845, 1995, 2205, 2475, 2565, 2805, 2835, 3003, 3045, 3285, 3315, 3465, 3645, 3675, 3885, 4095, 4125, 4275, 4347, 4455, 4515, 4725, 4995, 5115, 5355, 5445, 5733, 5775, 5805, 6045, 6195, 6237, 6405, 6435

Offset: 1

Jianing Song, Jan 12 2019

nonn

Numbers k such that k is in A067828 and that k - 1 is in A067825.
It's often the case that the sum of divisors for an odd number is less than at least one of its adjacent even numbers. This sequence lists the exceptions.
Most terms are congruent to 3 modulo 6. It seems that the smallest term not congruent to 3 modulo 6 is greater than 10^12.

			sigma(314) = 474, sigma(315) = 624, sigma(316) = 560, so 315 is a term.

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A000203, A067825, A067828;

Similar sequences: A076773, A323379.

Select[Range[1,8000,2],DivisorSigma[1,#] > DivisorSigma[1,(#+1)] && DivisorSigma[1,#] > DivisorSigma[1,(#-1)] &] (* K. D. Bajpai, Nov 19 2019 *)

forstep(n=3,2000,2,if(sigma(n)>sigma(n-1)&&sigma(n)>sigma(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

A323380 Odd n such that sigma(n) > sigma(n+1) and sigma(n) > sigma(n-1), sigma = A000203.

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