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A379229 Difference A003961(k)-(2*k) computed for the natural numbers k for which k and A003961(k) are relatively prime, where A003961 is fully multiplicative with a(prime(i)) = prime(i+1).

%I A379229 #8 Dec 23 2024 15:11:59
%S A379229 -1,-1,-1,1,-3,-3,11,7,1,-9,-9,5,49,-15,-15,23,13,-5,-17,-1,-1,71,43,
%T A379229 -27,-25,179,-1,-11,-33,-7,7,109,-39,-39,29,-5,-41,23,47,-7,49,-47,
%U A379229 -19,185,1,-23,-57,-55,-13,149,601,-11,-63,35,7,-69,-67,-25,55,-75,407,463,-35,-77,-37,-31,-19,175,-81,5,77,-1
%N A379229 Difference A003961(k)-(2*k) computed for the natural numbers k for which k and A003961(k) are relatively prime, where A003961 is fully multiplicative with a(prime(i)) = prime(i+1).
%H A379229 Antti Karttunen, <a href="/A379229/b379229.txt">Table of n, a(n) for n = 1..20000</a>
%H A379229 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.
%F A379229 a(n) = A252748(A319630(n)).
%o A379229 (PARI)
%o A379229 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A379229 A252748(n) = (A003961(n) - (2*n));
%o A379229 is_A319630(n) = (1==gcd(n,A003961(n)));
%o A379229 k=0; n=0; while(k<200, n++; if(is_A319630(n), print1(A252748(n),", ")));
%Y A379229 Cf. A003961, A252748, A319630.
%Y A379229 Cf. also A379230.
%K A379229 sign
%O A379229 1,5
%A A379229 _Antti Karttunen_, Dec 23 2024