cp's OEIS Frontend

A374223 Numbers k such that sigma(k) and sopfr(k) are both multiples of 3, where sigma is the sum of divisors, and sopfr is the sum of prime factors with repetition.

%I A374223 #10 Jul 08 2024 16:41:15
%S A374223 8,14,20,24,26,35,38,42,44,50,60,62,65,68,72,74,77,78,86,92,95,105,
%T A374223 110,114,116,119,122,125,126,132,134,143,146,150,155,158,160,161,164,
%U A374223 170,180,185,186,188,194,195,196,203,204,206,209,212,215,216,218,221,222,230,231,234,236,242,254,258,275,276,278,280
%N A374223 Numbers k such that sigma(k) and sopfr(k) are both multiples of 3, where sigma is the sum of divisors, and sopfr is the sum of prime factors with repetition.
%C A374223 Numbers such that the multiplicities of prime factors of the forms 3m+1 (A002476) and 3m-1 (A003627) are equal modulo 3, and some of the former has exponent of the form 3k+2, or some of the latter has odd exponent.
%C A374223 If m and n are in the sequence and gcd(m,n)=1, then m*n is also in sequence.
%C A374223 Term k is included <=> term 3*k is included.
%H A374223 Antti Karttunen, <a href="/A374223/b374223.txt">Table of n, a(n) for n = 1..12000</a>
%o A374223 (PARI) isA374223 = A374222;
%Y A374223 Cf. A000203, A001414, A002476, A003627, A374222 (characteristic function).
%Y A374223 Indices of multiples of 3 in A374126.
%Y A374223 Intersection of A087943 and A289142.
%K A374223 nonn
%O A374223 1,1
%A A374223 _Antti Karttunen_, Jul 08 2024