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

1,1

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.

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000203, A067825, A067828;

Similar sequences: A076773, A323379.

Sequence in context: A210889 A210891 A076648 * A256575 A295990 A349868

Adjacent sequences: A323377 A323378 A323379 * A323381 A323382 A323383

Keyword

nonn

Author

Jianing Song, Jan 12 2019

Status

approved