A349751 Odd numbers k such that sigma(k) == -k (mod 3), where sigma is the sum of divisors function.

7, 13, 15, 19, 31, 33, 37, 43, 45, 51, 61, 67, 69, 73, 79, 87, 97, 99, 103, 105, 109, 123, 127, 135, 139, 141, 147, 151, 153, 157, 159, 163, 165, 175, 177, 181, 193, 195, 199, 207, 211, 213, 223, 229, 231, 241, 249, 255, 261, 267, 271, 277, 283, 285, 297, 303, 307, 313, 315, 321, 325, 331, 337, 339, 345, 349, 357

Offset: 1

Author

Antti Karttunen, Nov 30 2021

Keywords

• nonn

Comments

Odd numbers k for which A155085(k) is a multiple of 3.

Examples

			7 is present as 7 mod 3 = +1, while sigma(7) = 8, and 8 mod 3 = 2, i.e., -1.
45 is present as 45 mod 3 = 0, while sigma(45) = 78, and 78 mod 3 = 0 as well.
		

Links

• Index entries for sequences where odd perfect numbers must occur, if they exist at all
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A010872, A074941, A155085, A349750.

Cf. A349752 (intersection with A349749).

Programs

Mathematica

Select[Range[1, 360, 2], Divisible[DivisorSigma[1, #] + #, 3] &] (* Amiram Eldar, Dec 01 2021 *)

PARI

isA349751(n) = ((n%2)&&0==(sigma(n)+n)%3);