cp's OEIS Frontend

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

%I A323726 #65 Sep 08 2022 08:46:23
%S A323726 3,63,75,135,147,195,255,399,459,483,495,555,567,615,627,663,675,735,
%T A323726 759,795,819,855,915,975,999,1035,1095,1215,1239,1287,1323,1455,1515,
%U A323726 1539,1647,1659,1683,1815,1827,1875,1935,2079,2115,2175,2235,2247,2295,2415,2499
%N A323726 Odd numbers k such that sigma(k-1) < sigma(k) < sigma(k+1), sigma(n) = A000203.
%C A323726 It appears that most of the terms are divisible by 3; the smallest exception is 13475.
%C A323726 Up to 10^9, 223182 of 20606497 (about 1%) of the terms are not divisible by 3. - _Charles R Greathouse IV_, Nov 28 2019
%H A323726 Robert Israel, <a href="/A323726/b323726.txt">Table of n, a(n) for n = 1..10000</a>
%e A323726 sigma(62) = 96, sigma(63) = 104, sigma(64) = 127. Hence, 63 is in the sequence.
%e A323726 sigma(74) = 114, sigma(75) = 124, sigma(76) = 140. Hence, 75 is in the sequence.
%p A323726 Sigmas:= map(numtheory:-sigma, [$1..3000]):
%p A323726 select(t -> Sigmas[t-1] < Sigmas[t] and Sigmas[t] < Sigmas[t+1],
%p A323726 [seq(i,i=3..3000,2)]); # _Robert Israel_, Nov 23 2019
%t A323726 Select[Range[1,8000,2], DivisorSigma[1, # - 1] < DivisorSigma[1, (#)] && DivisorSigma[1, #] < DivisorSigma[1, (# + 1)] &]
%o A323726 (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
%Y A323726 Cf. A000203, A005408, A053224, A067828, A323380.
%K A323726 nonn
%O A323726 1,1
%A A323726 _K. D. Bajpai_, Nov 19 2019