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A372566 Numbers k such that k, sigma(k) and A003961(k) have a common divisor larger than 1, where A003961(n) is fully multiplicative function with a(prime(i)) = prime(i+1).

%I A372566 #16 Dec 23 2024 16:29:28
%S A372566 6,18,24,30,42,54,60,66,72,78,90,96,102,114,120,126,132,135,138,140,
%T A372566 150,162,168,174,180,186,198,204,210,216,222,234,240,246,258,264,270,
%U A372566 276,282,285,288,294,306,312,318,330,342,348,354,360,366,378,384,390,396,402,408,414,420,426,435,438,450,455,456,462
%N A372566 Numbers k such that k, sigma(k) and A003961(k) have a common divisor larger than 1, where A003961(n) is fully multiplicative function with a(prime(i)) = prime(i+1).
%H A372566 Antti Karttunen, <a href="/A372566/b372566.txt">Table of n, a(n) for n = 1..12000</a>
%H A372566 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A372566 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%e A372566 24 = 2^3 * 3, sigma(24) = 60 = 2^2 * 3 * 5, and A003961(24) = 135 = 3^3 * 5, have 3 as their common divisor, therefore 24 is present in this sequence.
%o A372566 (PARI)
%o A372566 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A372566 isA372566(n) = (1<gcd([n, sigma(n), A003961(n)]));
%Y A372566 Cf. A000203, A003961.
%Y A372566 Positions of terms > 1 in A372565.
%Y A372566 Subsequence of each of the following sequences: A069059, A104210, A349166, A379477.
%Y A372566 Cf. A372567 (odd terms), A379475 (characteristic function).
%K A372566 nonn
%O A372566 1,1
%A A372566 _Antti Karttunen_, May 19 2024