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

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

1,1

Comments

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

Links

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

Example

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.

Maple

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A327053 A135444 A333041 * A087886 A123754 A377733

Adjacent sequences: A323723 A323724 A323725 * A323727 A323728 A323729

Keyword

nonn

Author

K. D. Bajpai, Nov 19 2019

Status

approved