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A323380
Odd n such that sigma(n) > sigma(n+1) and sigma(n) > sigma(n-1), sigma = A000203.
3
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
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
Similar sequences: A076773, A323379.
Sequence in context: A210889 A210891 A076648 * A256575 A295990 A349868
KEYWORD
nonn
AUTHOR
Jianing Song, Jan 12 2019
STATUS
approved