A349751 - OEIS

%I #11 Dec 04 2021 12:31:10

%S 7,13,15,19,31,33,37,43,45,51,61,67,69,73,79,87,97,99,103,105,109,123,

%T 127,135,139,141,147,151,153,157,159,163,165,175,177,181,193,195,199,

%U 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

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

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

%H <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

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

%e 45 is present as 45 mod 3 = 0, while sigma(45) = 78, and 78 mod 3 = 0 as well.

%t Select[Range[1, 360, 2], Divisible[DivisorSigma[1, #] + #, 3] &] (* _Amiram Eldar_, Dec 01 2021 *)

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

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

%Y Cf. A349752 (intersection with A349749).

%K nonn

%O 1,1

%A _Antti Karttunen_, Nov 30 2021