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%I #9 Nov 12 2021 22:34:55
%S 15,27,35,45,57,65,75,77,87,99,105,143,165,171,175,177,189,195,205,
%T 221,225,231,237,245,255,261,267,297,301,315,323,325,327,345,351,375,
%U 385,399,405,415,417,429,437,447,459,465,485,495,513,525,531,537,539,555,567,585,595,597,605,609,615,621,627,629,645
%N Odd numbers k for which gcd(k, A003961(k)) <> gcd(sigma(k), A003961(k)), where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors function.
%C Odd numbers for which A348994(n) <> A349161(n).
%C Equally, odd numbers such that A319626(n) <> A349164(n).
%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, 645, 2], GCD[#1, #3] != GCD[#2, #3] & @@ {#, 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 isA349175(n) = if(!(n%2),0,my(u=A003961(n)); gcd(u,sigma(n))!=gcd(u,n));
%Y Cf. A000203, A003961, A319626, A348994, A349161, A349164.
%Y Cf. A349169, A349174 (complement among the odd numbers).
%K nonn
%O 1,1
%A _Antti Karttunen_, Nov 10 2021
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