A324644 -id:A324644 - cp's OEIS frontend

A369446 Denominator of sigma(n) / A276086(n), where A276086 is the primorial base exp-function.

2, 1, 3, 9, 3, 5, 5, 1, 30, 5, 15, 25, 25, 25, 25, 225, 25, 125, 25, 125, 375, 125, 375, 125, 1250, 625, 375, 5625, 375, 7, 7, 1, 7, 7, 21, 5, 35, 7, 15, 7, 15, 175, 175, 25, 175, 175, 525, 875, 1750, 875, 875, 1125, 875, 875, 4375, 875, 2625, 875, 2625, 7, 49, 49, 147, 441, 21, 245, 245, 35, 245, 245, 245, 245, 1225

Offset: 1

Antti Karttunen, Jan 25 2024

Cf. A000203, A276086, A324644, A369445 (numerators).

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A369446(n) = { my(u=A276086(n)); (u/gcd(u,sigma(n))); };

a(n) = A276086(n) / A324644(n).

A379492 Multiperfect numbers k for which gcd(k,A003961(k))gcd(sigma(k),A276086(k)) is not equal to gcd(k,A276086(k))gcd(sigma(k),A003961(k)), where A003961(n) is fully multiplicative with a(prime(i)) = prime(i+1), and A276086 is the primorial base exp-function.

Original entry on oeis.org

120, 672, 523776, 1476304896, 14182439040, 31998395520, 518666803200, 13661860101120, 30823866178560, 740344994887680, 796928461056000, 212517062615531520, 69357059049509038080, 87934476737668055040, 154345556085770649600, 170206605192656148480, 1161492388333469337600, 1802582780370364661760, 9186050031556349952000

Offset: 1

Antti Karttunen, Jan 02 2025

nonn

Intersection of A007691 and A000027\A379486.
Cf. A000203, A003961, A276086, A322361, A324198, A324644, A342671, A379485, A379487, A379488, A379491 (complement in A007691).
Cf. A046061 (seems to be a subsequence), A323653.

isA379492(n) = (!(sigma(n)%n) && !A379485(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

A369446 Denominator of sigma(n) / A276086(n), where A276086 is the primorial base exp-function.

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A379492 Multiperfect numbers k for which gcd(k,A003961(k))gcd(sigma(k),A276086(k)) is not equal to gcd(k,A276086(k))gcd(sigma(k),A003961(k)), where A003961(n) is fully multiplicative with a(prime(i)) = prime(i+1), and A276086 is the primorial base exp-function.

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PARI

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

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Author

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PARI

Formula

cp's OEIS Frontend

A369446 Denominator of sigma(n) / A276086(n), where A276086 is the primorial base exp-function.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A379492 Multiperfect numbers k for which gcd(k,A003961(k))*gcd(sigma(k),A276086(k)) is not equal to gcd(k,A276086(k))*gcd(sigma(k),A003961(k)), where A003961(n) is fully multiplicative with a(prime(i)) = prime(i+1), and A276086 is the primorial base exp-function.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

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

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A379492 Multiperfect numbers k for which gcd(k,A003961(k))gcd(sigma(k),A276086(k)) is not equal to gcd(k,A276086(k))gcd(sigma(k),A003961(k)), where A003961(n) is fully multiplicative with a(prime(i)) = prime(i+1), and A276086 is the primorial base exp-function.