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

1,1

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

Table of n, a(n) for n=1..66.

Index entries for sequences where odd perfect numbers must occur, if they exist at all

Index entries for sequences related to sigma(n)

Mathematica

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

Prog

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

Crossrefs

Intersection of A349749 and A349751.

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

Sequence in context: A076196 A330431 A349751 * A167782 A326380 A257521

Adjacent sequences: A349749 A349750 A349751 * A349753 A349754 A349755

Keyword

nonn

Author

Antti Karttunen, Nov 30 2021

Status

approved