A323380 - OEIS

%I #16 Nov 18 2019 22:22:21

%S 315,405,525,693,765,945,1125,1155,1395,1575,1755,1785,1845,1995,2205,

%T 2475,2565,2805,2835,3003,3045,3285,3315,3465,3645,3675,3885,4095,

%U 4125,4275,4347,4455,4515,4725,4995,5115,5355,5445,5733,5775,5805,6045,6195,6237,6405,6435

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

%C Numbers k such that k is in A067828 and that k - 1 is in A067825.

%C 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.

%C 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.

%H K. D. Bajpai, <a href="/A323380/b323380.txt">Table of n, a(n) for n = 1..10000</a>

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

%t Select[Range[1,8000,2],DivisorSigma[1,#] > DivisorSigma[1,(#+1)] && DivisorSigma[1,#] > DivisorSigma[1,(#-1)] &] (* _K. D. Bajpai_, Nov 19 2019 *)

%o (PARI) forstep(n=3,2000,2,if(sigma(n)>sigma(n-1)&&sigma(n)>sigma(n+1), print1(n, ", ")))

%Y Cf. A000203, A067825, A067828;

%Y Similar sequences: A076773, A323379.

%K nonn

%O 1,1

%A _Jianing Song_, Jan 12 2019