A349752 - OEIS

%I #15 Dec 04 2021 12:31:19

%S 7,13,15,19,31,33,37,43,61,67,69,73,79,87,97,103,105,109,123,127,139,

%T 141,147,151,153,157,163,175,177,181,193,195,199,211,223,229,231,241,

%U 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

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

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

%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>

%t Select[Range[1, 463, 2], Divisible[(s = DivisorSigma[1, #]) + #, 3] && IntegerExponent[s, 3] == IntegerExponent[#, 3] &] (* _Amiram Eldar_, Dec 01 2021 *)

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

%Y Intersection of A349749 and A349751.

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

%K nonn

%O 1,1

%A _Antti Karttunen_, Nov 30 2021