A359269 -id:A359269 - cp's OEIS frontend

A359324 Number of divisors of 6n-2 of form 6k+5.

0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 2, 0, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 1, 0, 2, 1, 1, 0, 1, 1, 2, 0, 1, 0, 1, 2, 1, 1, 2, 0, 2, 0, 1, 0, 1, 2, 2, 0, 1, 0, 2, 0, 2, 1, 1, 2, 1, 1, 1, 0, 2, 1, 1, 0, 1, 1, 2, 0, 2, 1, 2, 0, 2, 0, 1, 2, 1, 1, 1, 1, 3, 0, 1, 0, 1, 2, 1, 0, 1

Offset: 1

Seiichi Manyama, Dec 25 2022

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A319995, A359305, A359325, A359326, A359327.

Cf. A359239, A359269, A359290.

a[n_] := DivisorSum[6*n-2, 1 &, Mod[#, 6] == 5 &]; Array[a, 100] (* Amiram Eldar, Aug 14 2023 *)

PARI
```
a(n) = sumdiv(6*n-2, d, d%6==5);
```

my(N=100, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(2*k)/(1-x^(6*k-1)))))

my(N=100, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(5*k-3)/(1-x^(6*k-4)))))

a(n) = A319995(6*n-2).
G.f.: Sum_{k>0} x^(2*k)/(1 - x^(6*k-1)).
G.f.: Sum_{k>0} x^(5*k-3)/(1 - x^(6*k-4)).

A359287 Number of divisors of 5n-1 of form 5k+2.

Original entry on oeis.org

1, 0, 2, 0, 2, 0, 2, 0, 2, 1, 2, 0, 2, 0, 2, 0, 4, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 3, 0, 4, 0, 2, 0, 2, 0, 2, 2, 2, 0, 4, 0, 2, 0, 4, 0, 2, 0, 2, 0, 2, 2, 4, 0, 2, 0, 2, 1, 4, 0, 2, 0, 2, 0, 4, 2, 2, 0, 2, 0, 2, 0, 4, 0, 4, 0, 4, 0, 2, 2, 2, 0, 2, 0, 2, 0, 4, 0, 4, 0

Offset: 1

Seiichi Manyama, Dec 24 2022

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A001877.
Cf. A359233, A359288.
Cf. A359237, A359244, A359269.

a[n_] := DivisorSum[5*n-1, 1 &, Mod[#, 5] == 2 &]; Array[a, 100] (* Amiram Eldar, Aug 16 2023 *)

PARI
```
a(n) = sumdiv(5*n-1, d, d%5==2);
```

my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^(2*k-1)/(1-x^(5*k-3))))

a(n) = A001877(5*n-1).

G.f.: Sum_{k>0} x^(2*k-1)/(1 - x^(5*k-3)).

A363025 Sum of divisors of 5n-2 of form 5k+2.

Original entry on oeis.org

0, 2, 0, 2, 0, 9, 0, 2, 0, 14, 0, 2, 7, 19, 0, 2, 0, 24, 0, 9, 0, 41, 0, 2, 0, 34, 7, 2, 0, 39, 17, 2, 0, 63, 0, 2, 0, 49, 0, 24, 7, 54, 0, 2, 0, 71, 0, 26, 27, 64, 0, 2, 0, 69, 7, 2, 0, 118, 0, 2, 0, 108, 0, 2, 17, 84, 37, 2, 7, 101, 0, 2, 0, 94, 0, 78, 0, 99, 0, 2, 0, 133, 7, 24, 47, 109, 0, 2, 0, 153, 0

Offset: 1

Seiichi Manyama, Jul 06 2023

nonn

Cf. A362952, A363026, A363027.

Cf. A284280, A359269, A363029.

a[n_] := DivisorSum[5*n - 2, # &, Mod[#, 5] == 2 &]; Array[a, 100] (* Amiram Eldar, Jul 06 2023 *)

PARI
```
a(n) = sumdiv(5*n-2, d, (d%5==2)*d);
```

a(n) = A284280(5*n-2).

G.f.: Sum_{k>0} (5*k-3) * x^(4*k-2) / (1 - x^(5*k-3)).

A364101 Sum of divisors of 5n-2 of form 5k+4.

Original entry on oeis.org

0, 4, 0, 9, 0, 18, 0, 19, 0, 28, 0, 29, 9, 38, 0, 39, 0, 48, 0, 63, 0, 67, 0, 59, 0, 68, 19, 69, 0, 78, 9, 79, 0, 126, 0, 89, 0, 98, 0, 108, 29, 108, 0, 109, 0, 137, 0, 167, 9, 128, 0, 129, 0, 138, 39, 139, 0, 181, 0, 149, 0, 216, 0, 159, 19, 168, 9, 169, 49, 207, 0, 179, 0, 188, 0, 266, 0, 198, 0

Offset: 1

Seiichi Manyama, Jul 04 2023

nonn

Cf. A364100, A364102, A364103.

Cf. A284103, A359269, A364105.

a[n_] := DivisorSum[5*n - 2, # &, Mod[#, 5] == 4 &]; Array[a, 100] (* Amiram Eldar, Jul 17 2023 *)

PARI
```
a(n) = sumdiv(5*n-2, d, (d%5==4)*d);
```

a(n) = A284103(5*n-2).

G.f.: Sum_{k>0} (5*k-1) * x^(2*k) / (1 - x^(5*k-1)).

A364105 Expansion of Sum_{k>0} k * x^(2k) / (1 - x^(5k-1)).

Original entry on oeis.org

0, 1, 0, 2, 0, 4, 0, 4, 0, 6, 0, 6, 2, 8, 0, 8, 0, 10, 0, 13, 0, 14, 0, 12, 0, 14, 4, 14, 0, 16, 2, 16, 0, 26, 0, 18, 0, 20, 0, 22, 6, 22, 0, 22, 0, 28, 0, 34, 2, 26, 0, 26, 0, 28, 8, 28, 0, 37, 0, 30, 0, 44, 0, 32, 4, 34, 2, 34, 10, 42, 0, 36, 0, 38, 0, 54, 0, 40, 0, 40, 0, 54, 12, 46, 2, 44, 0, 44, 0

Offset: 1

Seiichi Manyama, Jul 05 2023

nonn

Cf. A364104, A364106, A364107.

Cf. A359269, A364101.

a[n_] := DivisorSum[5*n - 2, # + 1 &, Mod[#, 5] == 4 &]/5; Array[a, 100] (* Amiram Eldar, Jul 12 2023 *)

a(n) = sumdiv(5*n-2, d, (d%5==4)*(d+1))/5;

a(n) = (1/5) * Sum_{d | 5*n-2, d==4 (mod 5)} (d+1).

G.f.: Sum_{k>0} x^(4*k-2) / (1 - x^(5*k-3))^2.

A363029 Expansion of Sum_{k>0} k * x^(4k-2) / (1 - x^(5k-3)).

Original entry on oeis.org

0, 1, 0, 1, 0, 3, 0, 1, 0, 4, 0, 1, 2, 5, 0, 1, 0, 6, 0, 3, 0, 10, 0, 1, 0, 8, 2, 1, 0, 9, 4, 1, 0, 15, 0, 1, 0, 11, 0, 6, 2, 12, 0, 1, 0, 16, 0, 7, 6, 14, 0, 1, 0, 15, 2, 1, 0, 26, 0, 1, 0, 24, 0, 1, 4, 18, 8, 1, 2, 22, 0, 1, 0, 20, 0, 18, 0, 21, 0, 1, 0, 29, 2, 6, 10, 23, 0, 1, 0, 33, 0, 1, 0

Offset: 1

Seiichi Manyama, Jul 06 2023

nonn

Cf. A359269, A363025.

a[n_] := DivisorSum[5*n - 2, # + 3 &, Mod[#, 5] == 2 &]/5; Array[a, 100] (* Amiram Eldar, Jul 06 2023 *)

a(n) = sumdiv(5*n-2, d, (d%5==2)*(d+3))/5;

a(n) = (1/5) * Sum_{d | 5*n-2, d==2 (mod 5)} (d+3).

G.f.: Sum_{k>0} x^(2*k) / (1 - x^(5*k-1))^2.

cp's OEIS Frontend

A359324 Number of divisors of 6*n-2 of form 6*k+5.

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A359287 Number of divisors of 5*n-1 of form 5*k+2.

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A363025 Sum of divisors of 5*n-2 of form 5*k+2.

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A364101 Sum of divisors of 5*n-2 of form 5*k+4.

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A364105 Expansion of Sum_{k>0} k * x^(2*k) / (1 - x^(5*k-1)).

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A363029 Expansion of Sum_{k>0} k * x^(4*k-2) / (1 - x^(5*k-3)).

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A359324 Number of divisors of 6n-2 of form 6k+5.

A359287 Number of divisors of 5n-1 of form 5k+2.

A363025 Sum of divisors of 5n-2 of form 5k+2.

A364101 Sum of divisors of 5n-2 of form 5k+4.

A364105 Expansion of Sum_{k>0} k * x^(2k) / (1 - x^(5k-1)).

A363029 Expansion of Sum_{k>0} k * x^(4k-2) / (1 - x^(5k-3)).