A359244 -id:A359244 - cp's OEIS frontend

A363027 Sum of divisors of 5n-4 of form 5k+2.

0, 2, 0, 2, 7, 2, 0, 14, 0, 2, 17, 9, 0, 24, 0, 2, 27, 2, 7, 46, 0, 2, 37, 2, 0, 51, 0, 19, 47, 2, 0, 66, 7, 2, 57, 24, 0, 64, 0, 9, 67, 2, 0, 113, 17, 2, 84, 2, 0, 84, 0, 34, 87, 9, 0, 106, 0, 24, 97, 39, 7, 121, 0, 2, 107, 2, 0, 175, 0, 2, 144, 2, 0, 124, 7, 49, 127, 2, 17, 168, 0, 9, 137, 86, 0, 144, 0, 2

Offset: 1

Seiichi Manyama, Jul 06 2023

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A362952, A363025, A363026.

Cf. A284280, A359244, A363032.

f:= n ->
  convert(select(t -> t mod 5 = 2, numtheory:-divisors(5*n-4)),`+`):
map(f, [$1..100]); # Robert Israel, Jul 23 2023

a[n_] := DivisorSum[5*n - 4, # &, Mod[#, 5] == 2 &]; Array[a, 100] (* Amiram Eldar, Jul 06 2023 *)
Table[Total[Select[Divisors[5n-4],Mod[#,5]==2&]],{n,90}] (* Harvey P. Dale, Feb 01 2025 *)

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

a(n) = A284280(5*n-4).

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

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)).

A359288 Number of divisors of 5n-1 of form 5k+3.

Original entry on oeis.org

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

Offset: 1

Seiichi Manyama, Dec 24 2022

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

Cf. A001878.
Cf. A359233, A359287.
Cf. A359236, A359244, A359270.

a[n_] := DivisorSum[5*n-1, 1 &, Mod[#, 5] == 3 &]; Array[a, 100] (* Amiram Eldar, Aug 16 2023 *)

PARI
```
a(n) = sumdiv(5*n-1, d, d%5==3);
```

my(N=100, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(3*k-1)/(1-x^(5*k-2)))))

a(n) = A001878(5*n-1).

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

A363053 Sum of divisors of 5n-4 of form 5k+3.

Original entry on oeis.org

0, 3, 0, 8, 3, 13, 0, 21, 0, 23, 3, 36, 0, 36, 0, 38, 3, 43, 13, 59, 0, 53, 3, 58, 0, 84, 0, 76, 3, 73, 0, 94, 23, 83, 3, 96, 0, 96, 0, 126, 3, 103, 0, 137, 13, 113, 36, 118, 0, 126, 0, 136, 3, 171, 0, 164, 0, 156, 3, 156, 43, 174, 0, 158, 3, 163, 0, 255, 0, 173, 16, 178, 0, 186, 53, 196, 3, 193, 23, 252

Offset: 1

Seiichi Manyama, Jul 06 2023

nonn

Cf. A363033, A363034, A363035.

Cf. A284281, A359244, A363158.

a[n_] := DivisorSum[5*n - 4, # &, Mod[#, 5] == 3 &]; Array[a, 100] (* Amiram Eldar, Jul 06 2023 *)

PARI
```
a(n) = sumdiv(5*n-4, d, (d%5==3)*d);
```

a(n) = A284281(5*n-4).

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

A363032 Expansion of Sum_{k>0} k * x^(3k-1) / (1 - x^(5k-3)).

Original entry on oeis.org

0, 1, 0, 1, 2, 1, 0, 4, 0, 1, 4, 3, 0, 6, 0, 1, 6, 1, 2, 11, 0, 1, 8, 1, 0, 12, 0, 5, 10, 1, 0, 15, 2, 1, 12, 6, 0, 14, 0, 3, 14, 1, 0, 25, 4, 1, 18, 1, 0, 18, 0, 8, 18, 3, 0, 23, 0, 6, 20, 9, 2, 26, 0, 1, 22, 1, 0, 38, 0, 1, 30, 1, 0, 26, 2, 11, 26, 1, 4, 36, 0, 3, 28, 19, 0, 30, 0, 1, 32, 1, 0, 47, 0

Offset: 1

Seiichi Manyama, Jul 06 2023

nonn

Cf. A359244, A363027.

a[n_] := DivisorSum[5*n - 4, # + 3 &, Mod[#, 5] == 2 &]/5; Array[a, 100] (* Amiram Eldar, Jul 06 2023 *)

a(n) = sumdiv(5*n-4, d, (d%5==2)*(d+3))/5;

a(n) = (1/5) * Sum_{d | 5*n-4, d==2 (mod 5)} (d+3).

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

A363158 Expansion of Sum_{k>0} k * x^(2k) / (1 - x^(5k-2)).

Original entry on oeis.org

0, 1, 0, 2, 1, 3, 0, 5, 0, 5, 1, 8, 0, 8, 0, 8, 1, 9, 3, 13, 0, 11, 1, 12, 0, 18, 0, 16, 1, 15, 0, 20, 5, 17, 1, 20, 0, 20, 0, 26, 1, 21, 0, 29, 3, 23, 8, 24, 0, 26, 0, 28, 1, 35, 0, 34, 0, 32, 1, 32, 9, 36, 0, 32, 1, 33, 0, 53, 0, 35, 4, 36, 0, 38, 11, 40, 1, 39, 5, 52, 0, 53, 1, 47, 0, 44, 0

Offset: 1

Seiichi Manyama, Jul 06 2023

nonn

Cf. A359244, A363053.

a[n_] := DivisorSum[5*n - 4, # + 2 &, Mod[#, 5] == 3 &]/5; Array[a, 100] (* Amiram Eldar, Jul 06 2023 *)

a(n) = sumdiv(5*n-4, d, (d%5==3)*(d+2))/5;

a(n) = (1/5) * Sum_{d | 5*n-4, d==3 (mod 5)} (d+2).

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

cp's OEIS Frontend

A363027 Sum of divisors of 5*n-4 of form 5*k+2.

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

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A359288 Number of divisors of 5*n-1 of form 5*k+3.

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A363053 Sum of divisors of 5*n-4 of form 5*k+3.

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A363032 Expansion of Sum_{k>0} k * x^(3*k-1) / (1 - x^(5*k-3)).

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A363158 Expansion of Sum_{k>0} k * x^(2*k) / (1 - x^(5*k-2)).

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A363027 Sum of divisors of 5n-4 of form 5k+2.

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

A359288 Number of divisors of 5n-1 of form 5k+3.

A363053 Sum of divisors of 5n-4 of form 5k+3.

A363032 Expansion of Sum_{k>0} k * x^(3k-1) / (1 - x^(5k-3)).

A363158 Expansion of Sum_{k>0} k * x^(2k) / (1 - x^(5k-2)).