A349752 Odd numbers k for which the sigma(k) == -k (mod 3) and sigma(k) preserves the 3-adic valuation of k.

7, 13, 15, 19, 31, 33, 37, 43, 61, 67, 69, 73, 79, 87, 97, 103, 105, 109, 123, 127, 139, 141, 147, 151, 153, 157, 163, 175, 177, 181, 193, 195, 199, 211, 223, 229, 231, 241, 249, 271, 277, 283, 285, 303, 307, 313, 325, 331, 337, 339, 349, 367, 373, 375, 379, 393, 397, 409, 411, 421, 429, 433, 439, 447, 457, 463

Offset: 1

Author

Antti Karttunen, Nov 30 2021

Keywords

• nonn

Comments

Incidentally, of the 37 known terms of A228059, all of which are multiples of three, only 15 (less than half) satisfy this condition.

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

Intersection of A349749 and A349751.

Cf. A000203, A007949, A010872, A074941, A228059, A329963, A349750.

Programs

Mathematica

Select[Range[1, 463, 2], Divisible[(s = DivisorSigma[1, #]) + #, 3] && IntegerExponent[s, 3] == IntegerExponent[#, 3] &] (* Amiram Eldar, Dec 01 2021 *)

PARI

isA349752(n) = ((n%2) && (0==(sigma(n)+n)%3) && valuation(sigma(n), 3)==valuation(n, 3));