A355002 - OEIS

%I #7 Jul 17 2022 15:21:00

%S 135,140,285,435,455,675,700,855,885,910,945,980,1120,1185,1305,1335,

%T 1365,1425,1435,1485,1540,1635,1755,1820,1995,2085,2175,2235,2275,

%U 2295,2380,2565,2574,2655,2660,2685,2870,2905,2985,3045,3105,3135,3185,3220,3311,3375,3395,3435,3500,3555,3585,3640,3705,3915,4005

%N Numbers k that share a prime factor with A355456(k).

%C Numbers k such that A324198(k) and A342671(k) are not relatively prime.

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A355442(n) = gcd(A003961(n), A276086(n));

%o A355456(n) = gcd(sigma(n), A355442(n));

%o isA355002(n) = (1!=gcd(n,A355456(n)));

%Y Cf. A000203, A003961, A276086, A324644, A342671, A351459, A355442, A355456.

%Y Subsequence of A324584 and of A349166.

%K nonn

%O 1,1

%A _Antti Karttunen_, Jul 13 2022