A355456 -id:A355456 - cp's OEIS frontend

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

Antti Karttunen, Jul 13 2022

nonn

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

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

Subsequence of A324584 and of A349166.

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)));

A355442 a(n) = gcd(A003961(n), A276086(n)), where A003961 is fully multiplicative with a(p) = nextprime(p), and A276086 is primorial base exp-function.

Original entry on oeis.org

1, 3, 1, 9, 1, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5, 9, 1, 25, 1, 3, 5, 3, 1, 5, 1, 3, 125, 9, 1, 7, 1, 3, 1, 3, 7, 5, 1, 3, 5, 63, 1, 5, 1, 3, 175, 3, 1, 5, 1, 21, 5, 9, 1, 125, 7, 3, 5, 3, 1, 7, 1, 3, 1, 9, 7, 5, 1, 3, 5, 21, 1, 25, 1, 3, 245, 9, 1, 5, 1, 21, 125, 3, 1, 5, 7, 3, 5, 9, 1, 7, 1, 3, 1, 3, 7, 5, 1, 3, 5, 441

Offset: 1

Antti Karttunen, Jul 13 2022

nonn

Antti Karttunen, Table of n, a(n) for n = 1..11550
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences computed from indices in prime factorization
Index entries for sequences related to primorial base

Cf. A003961, A020639, A276086, A355001 [smallest prime factor of a(n)], A355456 [= gcd(sigma(n), a(n))], A355692 (Dirichlet inverse), A355820, A355821 (positions of 1's).

Cf. also A322361, A324198, A351459.

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));

a(n) = gcd(A003961(n), A276086(n)).

A355818 Greatest common divisor of n, sigma(n) and A276086(n), where A276086 is primorial base exp-function.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 3, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3

Offset: 1

Antti Karttunen, Jul 19 2022

nonn

Sequence contains only terms of A048103.
Cf. A000203, A009194, A276086, A324198, A324644.
Cf. also A355815, A327858, A355456.

A009194(n) = gcd(n, sigma(n));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A355818(n) = gcd(A009194(n), A276086(n));

a(n) = gcd(n, A324644(n)) = gcd(A000203(n), A324198(n)) = gcd(A009194(n), A276086(n)).

a(n) = gcd(A009194(n), A324198(n)).

cp's OEIS Frontend

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

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A355442 a(n) = gcd(A003961(n), A276086(n)), where A003961 is fully multiplicative with a(p) = nextprime(p), and A276086 is primorial base exp-function.

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A355818 Greatest common divisor of n, sigma(n) and A276086(n), where A276086 is primorial base exp-function.

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