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%I #13 Nov 12 2021 22:35:07
%S 1,3,5,7,9,11,13,17,19,21,23,25,29,31,33,37,39,41,43,47,49,51,53,55,
%T 59,61,63,67,69,71,73,79,81,83,85,89,91,93,95,97,101,103,107,109,111,
%U 113,115,117,119,121,123,125,127,129,131,133,137,139,141,145,147,149,151,153,155,157,159,161,163,167,169,173
%N Odd numbers k for which gcd(k, A003961(k)) = gcd(sigma(k), A003961(k)) = 1, where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors function.
%C Odd numbers k for which k and A003961(k) are relatively prime, and also sigma(k) and A003961(k) are coprime.
%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>
%t Select[Range[1, 173, 2], GCD[#1, #3] == GCD[#2, #3] == 1 & @@ {#, DivisorSigma[1, #], Times @@ Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]]} &] (* _Michael De Vlieger_, Nov 11 2021 *)
%o (PARI)
%o A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o isA349177(n) = if(!(n%2),0,my(u=A003961(n),t=gcd(u,n)); (1==t)&&(gcd(u,sigma(n))==t));
%Y Subsequence of A349174 from this first differs by not having term 135 (see A349176).
%Y Intersection of A319630 and A349174, or equally, intersection of A349165 and A349174.
%Y Cf. A000203, A003961, A319626, A348994, A349161, A349164, A349169.
%K nonn
%O 1,2
%A _Antti Karttunen_, Nov 11 2021
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