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A361627 Positive integers such that GCD(A007504(n),n) != 1.

%I A361627 #18 Mar 22 2023 15:18:08
%S A361627 18,23,24,25,30,36,42,53,54,56,57,63,78,84,85,90,99,105,111,117,123,
%T A361627 126,129,138,154,170,177,180,190,195,207,213,222,228,230,237,238,240,
%U A361627 245,246,252,258,270,273,275,276,282,288,297,299,303,304,309,318,319,322,327,333,339,345
%N A361627 Positive integers such that GCD(A007504(n),n) != 1.
%C A361627 A301274(k) != k implies that k is a term of this sequence.
%C A361627 Conjecture: a(n) ~ C*n as n -> infinity, where 5.25 < C < 5.35.
%e A361627 18 is a term of this sequence since the sum of the first 18 primes is 501 and GCD(501,18) = 3 != 1.
%t A361627 s[n_] := Sum[Prime[k], {k, 1, n}];
%t A361627 Complement[Table[n, {n, 1, 1000}], Flatten[Position[Table[GCD[s[n], n], {n, 1, 1000}], 1]]]
%o A361627 (PARI) isok(k) = gcd(vecsum(primes(k)), k) != 1; \\ _Michel Marcus_, Mar 18 2023
%o A361627 (Python)
%o A361627 from math import gcd
%o A361627 from itertools import count, islice
%o A361627 from sympy import nextprime
%o A361627 def A361627_gen(): # generator of terms
%o A361627     p, s = 2, 2
%o A361627     for n in count(1):
%o A361627         if gcd(n,s) > 1:
%o A361627             yield n
%o A361627         s += (p:=nextprime(p))
%o A361627 A361627_list = list(islice(A361627_gen(),20)) # _Chai Wah Wu_, Mar 22 2023
%Y A361627 Cf. A007504, A301274.
%K A361627 nonn
%O A361627 1,1
%A A361627 _Luca Onnis_, Mar 18 2023