A295310 -id:A295310 - cp's OEIS frontend

A295311 a(n) = n / A295310(n) = n / gcd(n, phi(sigma(n))).

1, 1, 3, 2, 5, 3, 7, 1, 3, 5, 11, 1, 13, 7, 15, 8, 17, 3, 19, 5, 21, 11, 23, 3, 5, 13, 27, 7, 29, 5, 31, 8, 33, 17, 35, 1, 37, 19, 13, 5, 41, 21, 43, 11, 15, 23, 47, 4, 49, 5, 17, 26, 53, 27, 55, 7, 57, 29, 59, 5, 61, 31, 21, 32, 65, 11, 67, 17, 69, 35, 71, 3, 73, 37, 5, 19, 77, 13, 79, 4, 81, 41, 83, 7, 85, 43, 87, 11, 89, 5

Offset: 1

Antti Karttunen, Nov 22 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384

Cf. A000010, A000203, A062401, A295301, A295310, A295312, A295314.

a(n) = n/gcd(n, eulerphi(sigma(n))); \\ Michel Marcus, Nov 23 2017

A295312 a(n) = A062401(n) / A295310(n) = phi(sigma(n)) / gcd(n, phi(sigma(n))).

Original entry on oeis.org

1, 1, 2, 3, 2, 2, 4, 1, 4, 3, 4, 1, 6, 4, 8, 15, 6, 4, 8, 3, 16, 6, 8, 2, 6, 6, 16, 6, 8, 4, 16, 9, 16, 9, 16, 2, 18, 8, 8, 3, 12, 16, 20, 6, 8, 12, 16, 5, 36, 6, 8, 21, 18, 16, 24, 4, 32, 12, 16, 4, 30, 16, 16, 63, 24, 8, 32, 9, 32, 24, 24, 4, 36, 18, 4, 12, 32, 8, 32, 3, 110, 18, 24, 8, 36, 20, 32, 6, 24, 4, 48, 12, 64, 24, 32, 3

Offset: 1

Antti Karttunen, Nov 22 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384

Cf. A000010, A000203, A062401, A295301, A295310, A295311, A295315.

a(n) = my(fsn = eulerphi(sigma(n))); fsn/gcd(n, fsn); \\ Michel Marcus, Nov 23 2017

a(n) = A000010(A000203(n)) / gcd(n, A000010(A000203(n))).

A353751 a(n) = gcd(n, sigma(sigma(n))), where sigma is the sum of divisors function.

Original entry on oeis.org

1, 2, 1, 4, 1, 2, 1, 8, 1, 1, 1, 4, 1, 2, 15, 16, 1, 2, 1, 4, 21, 1, 1, 24, 1, 2, 9, 4, 1, 15, 1, 8, 1, 2, 1, 4, 1, 2, 3, 2, 1, 42, 1, 4, 3, 1, 1, 16, 1, 2, 3, 1, 1, 18, 5, 8, 3, 2, 1, 60, 1, 2, 21, 64, 1, 1, 1, 4, 3, 1, 1, 24, 1, 2, 1, 4, 7, 6, 1, 16, 1, 2, 1, 84, 5, 2, 3, 2, 1, 6, 1, 4, 3, 1, 5, 8, 1, 2, 1, 4

Offset: 1

Antti Karttunen, May 08 2022

nonn

Index entries for sequences related to sigma(n)

Cf. A000203, A051027, A318059, A318060.
Cf. A019278 (positions of fixed points, where a(n)=n).
Cf. also A009194, A295310.

PARI
```
A353751(n) = gcd(n, sigma(sigma(n)));
```

a(n) = gcd(n, A051027(n)).

a(n) = A051027(n) / A318059(n) = n / A318060(n).

cp's OEIS Frontend

A295311 a(n) = n / A295310(n) = n / gcd(n, phi(sigma(n))).

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A295312 a(n) = A062401(n) / A295310(n) = phi(sigma(n)) / gcd(n, phi(sigma(n))).

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Formula

A353751 a(n) = gcd(n, sigma(sigma(n))), where sigma is the sum of divisors function.

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Author

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PARI

Formula