A355002 Numbers k that share a prime factor with A355456(k).

135, 140, 285, 435, 455, 675, 700, 855, 885, 910, 945, 980, 1120, 1185, 1305, 1335, 1365, 1425, 1435, 1485, 1540, 1635, 1755, 1820, 1995, 2085, 2175, 2235, 2275, 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

Offset: 1

Author

Antti Karttunen, Jul 13 2022

Keywords

• nonn

Comments

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

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial base
• Index entries for sequences related to sigma(n)

Crossrefs

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

Subsequence of A324584 and of A349166.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A355442(n) = gcd(A003961(n), A276086(n));
A355456(n) = gcd(sigma(n), A355442(n));
isA355002(n) = (1!=gcd(n,A355456(n)));