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

Author

Jianing Song, Jan 12 2019

Keywords

• nonn

Comments

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.

Examples

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

Links

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

Crossrefs

Cf. A000203, A067825, A067828;

Similar sequences: A076773, A323379.

Programs

Mathematica

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

PARI

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