A241029 -id:A241029 - cp's OEIS frontend

A241030 Sum of n-th powers of divisors of 26.

4, 42, 850, 19782, 485554, 12252702, 313742650, 8094558822, 209642795554, 5440108178862, 141304954146250, 3672136647383862, 95452254746808754, 2481455748310337022, 64513912079682866650, 1677310528178740048902, 43609408316038057305154

Offset: 0

Vincenzo Librandi, Apr 17 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (42,-457,1092,-676).

Cf. similar sequences listed in A241029.

Magma
```
[DivisorSigma(n, 26): n in [0..20]];
```

Total[#^Range[0, 20] & /@ Divisors[26]] (* or *) Table[(1 + 2^n) (1 + 13^n), {n, 0, 20}]

G.f.: 2*(2 - 63*x + 457*x^2 - 546*x^3)/((1 - x)*(1 - 2*x)*(1 - 13*x)*(1 - 26*x)).

a(n) = (1 + 2^n)*(1 + 13^n).

A241031 Sum of n-th powers of divisors of 28.

Original entry on oeis.org

6, 56, 1050, 25112, 655746, 17766056, 489541650, 13599182072, 379283617986, 10599157616456, 296486304875250, 8297561014164632, 232274972859656226, 6502905234227329256, 182070232515259616850, 5097810928082584052792

Offset: 0

Vincenzo Librandi, Apr 17 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (56,-1043,8240,-29204,43904,-21952).

Cf. A018254 (divisors of 28).

Cf. similar sequence listed in A241029.

Magma
```
[DivisorSigma(n, 28): n in [0..20]];
```
Magma
```
[(4^n+2^n+1)*(7^n+1): n in [0..20]];
```

Total[#^Range[0, 20] & /@ Divisors[28]] (* or *) Table[(4^n + 2^n + 1) (7^n + 1), {n, 0, 20}]

G.f.: 2*(3 - 140*x + 2086*x^2 - 12360*x^3 + 29204*x^4 - 21952*x^5)/((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 7*x)*(1 - 14*x)*(1 - 28*x)).

a(n) = (4^n + 2^n + 1)*(7^n + 1).

A241032 Sum of n-th powers of divisors of 30.

Original entry on oeis.org

8, 72, 1300, 31752, 872644, 25170552, 741453700, 22051219752, 658764967684, 19722455410392, 591076720682500, 17723450167663752, 531571748759349124, 15945186209351359032, 478326193010497869700, 14349345894391097803752

Offset: 0

Vincenzo Librandi, Apr 17 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (72,-1942,25992,-190081,779760,-1747800,1944000,-810000).

Cf. A018255 (divisors of 30).

Cf. similar sequence listed in A241029.

Magma
```
[DivisorSigma(n, 30): n in [0..20]];
```
Mathematica
```
Total[#^Range[0, 20] & /@ Divisors[30]]
```

G.f.: (8 - 504*x + 11652*x^2 - 129960*x^3 + 760324*x^4 - 2339280* x^5 + 3495600*x^6 - 1944000*x^7) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 5*x)*(1 - 6*x)*(1 - 10*x)*(1 - 15*x)*(1 - 30*x)).

a(n) = (1 + 2^n)*(1 + 3^n)*(1 + 5^n).

cp's OEIS Frontend

A241030 Sum of n-th powers of divisors of 26.

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A241031 Sum of n-th powers of divisors of 28.

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Magma

Magma

Mathematica

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A241032 Sum of n-th powers of divisors of 30.

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Magma

Mathematica

Formula