A339966 -id:A339966 - cp's OEIS frontend

A339964 a(n) = gcd(sigma(n), n+1).

1, 3, 4, 1, 6, 1, 8, 3, 1, 1, 12, 1, 14, 3, 8, 1, 18, 1, 20, 21, 2, 1, 24, 5, 1, 3, 4, 1, 30, 1, 32, 3, 2, 1, 12, 1, 38, 3, 8, 1, 42, 1, 44, 3, 2, 1, 48, 1, 1, 3, 4, 1, 54, 5, 8, 3, 2, 1, 60, 1, 62, 3, 8, 1, 6, 1, 68, 3, 2, 1, 72, 1, 74, 3, 4, 7, 6, 1, 80, 3, 1, 1, 84, 1, 2, 3, 8, 1, 90, 13, 4, 3, 2, 1, 24, 1, 98, 9, 4, 1, 102

Offset: 1

Antti Karttunen, Dec 25 2020

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to sigma(n)

Cf. A000203, A009194, A339965, A339966.
Cf. A339963 (positions of 2's).
Cf. also A049559, A062754.

PARI
```
A339964(n) = gcd(sigma(n),n+1);
```

A339965 a(n) = sigma(n) / gcd(sigma(n),n+1).

Original entry on oeis.org

1, 1, 1, 7, 1, 12, 1, 5, 13, 18, 1, 28, 1, 8, 3, 31, 1, 39, 1, 2, 16, 36, 1, 12, 31, 14, 10, 56, 1, 72, 1, 21, 24, 54, 4, 91, 1, 20, 7, 90, 1, 96, 1, 28, 39, 72, 1, 124, 57, 31, 18, 98, 1, 24, 9, 40, 40, 90, 1, 168, 1, 32, 13, 127, 14, 144, 1, 42, 48, 144, 1, 195, 1, 38, 31, 20, 16, 168, 1, 62, 121, 126, 1, 224, 54, 44

Offset: 1

Antti Karttunen, Dec 25 2020

Antti Karttunen, Table of n, a(n) for n = 1..10080
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences related to sigma(n)

Cf. A000203, A339964, A339966 (denominators).
Cf. A017665.
Cf. also A160595.

Table[DivisorSigma[1, n]/GCD[DivisorSigma[1, n], n + 1], {n, 80}] (* Wesley Ivan Hurt, Oct 10 2021 *)

A339965(n) = sigma(n)/(gcd(sigma(n),n+1));

a(n) = A000203(n) / A339964(n).

a(n) = numerator(sigma(n)/(n+1)). - Michel Marcus, Jan 07 2023

A359625 Least number m such that denominator(sigma(m)/(m+1)) = n, or zero if no such m exists.

Original entry on oeis.org

2, 1, 8, 95, 4, 143, 6, 63, 26, 9, 10, 16415, 12, 111, 44, 255, 16, 273023, 18, 159, 62, 175, 22, 575, 74, 25, 80, 671, 28, 3599, 30, 511, 395, 441, 34, 5183, 36, 303, 116, 8639, 40, 163295, 42, 1055, 134, 101567, 46, 19191876318719, 48, 49, 152, 415, 52, 3887

Offset: 1

Michel Marcus, Jan 07 2023

nonn

First occurrence of n in A339966.

Martin Ehrenstein, Table of n, a(n) for n = 1..10000 (first 1000 terms, except for n = 48, from Michel Marcus)

Cf. A162657 (analog for sigma(m)/m), A339966.

Cf. A063906 (sigma(m)/(m+1) = 3/2)

a(n) = my(k=1); while (denominator(sigma(k)/(k+1)) != n, k++); k;

a(n) = if(n == 1, return(2)); my(k=n-1); while (denominator(sigma(k)/(k+1)) != n, k+=n); k; \\ David A. Corneth, Jan 12 2023

n | (a(n) + 1). - David A. Corneth, Jan 12 2023

a(48)-a(54) from Martin Ehrenstein, Jul 23 2023

cp's OEIS Frontend

A339964 a(n) = gcd(sigma(n), n+1).

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A339965 a(n) = sigma(n) / gcd(sigma(n),n+1).

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A359625 Least number m such that denominator(sigma(m)/(m+1)) = n, or zero if no such m exists.

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