cp's OEIS Frontend

A349144 Numbers k for which A342671(k) [= gcd(sigma(k), A003961(k))] and A349161(k) [= A003961(k)/A342671(k)] are relatively prime, where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors function.

%I A349144 #14 Jan 09 2024 13:17:07
%S A349144 1,2,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,21,22,23,25,26,28,29,
%T A349144 30,31,33,34,35,36,37,38,39,41,42,43,45,46,47,48,49,50,51,52,53,55,57,
%U A349144 58,59,61,62,63,64,65,66,67,68,69,70,71,73,74,75,76,77,78,79,81,82,83,84,85,86,87,89,90,91,93,94,95
%N A349144 Numbers k for which A342671(k) [= gcd(sigma(k), A003961(k))] and A349161(k) [= A003961(k)/A342671(k)] are relatively prime, where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors function.
%C A349144 Numbers k for which A349163(k) and A349164(k) are coprime, i.e., k such that A349163(k) and A349164(k) are unitary divisors of k.
%H A349144 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A349144 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t A349144 Select[Range[95], GCD[#2, #1/#2] == 1 & @@ {#2, #2/GCD[##]} & @@ {DivisorSigma[1, #], If[# == 1, 1, Times @@ Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]]]} &] (* _Michael De Vlieger_, Nov 11 2021 *)
%o A349144 (PARI)
%o A349144 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A349144 isA349144(n) = { my(u=A003961(n), x=gcd(u,sigma(n))); (1==gcd(x,u/x)); };
%Y A349144 Cf. A000203, A003961, A342671, A349161, A349163, A349164.
%Y A349144 Complement of A349168.
%Y A349144 Cf. A349165 (subsequence).
%K A349144 nonn
%O A349144 1,2
%A A349144 _Antti Karttunen_, Nov 11 2021