%I #10 Nov 10 2021 18:26:13

%S 2,6,8,10,14,18,20,22,24,26,27,30,32,34,38,40,42,44,46,50,54,56,57,58,

%T 60,62,65,66,68,70,72,74,78,80,82,86,87,88,90,92,94,96,98,99,100,102,

%U 104,106,108,110,114,116,118,120,122,126,128,130,132,134,135,136,138,140,142,146,150,152,154,158,160,162,164

%N Numbers k such that sigma(k) and A003961(k) share a prime factor, where A003961(n) is fully multiplicative function with a(prime(k)) = prime(k+1).

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

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

%e For n = 2, A000203(2) = A003961(2) = 3, therefore they share a prime factor 3, and 2 is included in this sequence.

%e For n = 10 = 2*5, sigma(10) = 18 = 2 * 3^2, while A003961(10) = 21 = 3*7, therefore 10 is included, as there is a shared prime factor (3).

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o isA349166(n) = (1!=gcd(sigma(n), A003961(n)));

%Y Cf. A000203, A003961.

%Y Positions of terms larger than ones in A342671, and also in A349163.

%Y Positions of zeros in A349167.

%Y Cf. A349165 (complement), A349168 (subsequence).

%K nonn

%O 1,1

%A _Antti Karttunen_, Nov 09 2021