A017712 -id:A017712 - cp's OEIS frontend

A013959 a(n) = sigma_11(n), the sum of the 11th powers of the divisors of n.

1, 2049, 177148, 4196353, 48828126, 362976252, 1977326744, 8594130945, 31381236757, 100048830174, 285311670612, 743375541244, 1792160394038, 4051542498456, 8649804864648, 17600780175361, 34271896307634, 64300154115093, 116490258898220, 204900053024478

Offset: 1

N. J. A. Sloane

If the canonical factorization of n into prime powers is the product of p^e(p) then sigma_k(n) = Product_p ((p^((e(p)+1)*k))-1)/(p^k-1).
Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001
Related to congruence properties of the Ramanujan tau function since A000594(n) == a(n) (mod 691) = A046694(n). - Benoit Cloitre, Aug 28 2002

T. D. Noe, Table of n, a(n) for n=1..1000
Index entries for sequences related to sigma(n).

Cf. A000594, A027860, A046694.

Cf. A000203, A001157-A001160, A013670, A013954-A013972, A017665-A017712.

[DivisorSigma(11, n): n in [1..20]]; // Vincenzo Librandi, Sep 10 2016

Table[DivisorSigma[11, n], {n, 30}] (* Vincenzo Librandi, Sep 10 2016 *)

a(n)=sigma(n,11) \\ Charles R Greathouse IV, Apr 28 2011

my(N=99, q='q+O('q^N)); Vec(sum(n=1, N, n^11*q^n/(1-q^n))) \\ Altug Alkan, Sep 10 2016

from sympy import divisor_sigma
def A013959(n): return divisor_sigma(n,11) # Chai Wah Wu, Nov 17 2022

[sigma(n,11)for n in range(1,18)] # Zerinvary Lajos, Jun 04 2009

G.f.: Sum_{k>=1} k^11*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003
Dirichlet g.f.: zeta(s-11)*zeta(s). - Ilya Gutkovskiy, Sep 10 2016
From Amiram Eldar, Oct 29 2023: (Start)
Multiplicative with a(p^e) = (p^(11*e+11)-1)/(p^11-1).
Sum_{k=1..n} a(k) = zeta(12) * n^12 / 12 + O(n^13). (End)

A013957 a(n) = sigma_9(n), the sum of the 9th powers of the divisors of n.

Original entry on oeis.org

1, 513, 19684, 262657, 1953126, 10097892, 40353608, 134480385, 387440173, 1001953638, 2357947692, 5170140388, 10604499374, 20701400904, 38445332184, 68853957121, 118587876498, 198756808749, 322687697780, 513002215782, 794320419872, 1209627165996, 1801152661464

Offset: 1

N. J. A. Sloane

If the canonical factorization of n into prime powers is the product of p^e(p) then sigma_k(n) = Product_p ((p^((e(p)+1)*k))-1)/(p^k-1).
Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001
Note that the sequence is not monotonically increasing, with a(4488) > a(4489) being the first of infinitely many examples. - Charles R Greathouse IV, Dec 28 2021

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
T. H. Grönwall, Some asymptotic expressions in the Theory of Numbers, Trans. Amer. Math. Soc., Vol. 14, No. 1 (1913), pp. 113-122.
Index entries for sequences related to sigma(n).

Cf. A000203, A001157-A001160, A013667, A013668, A013954-A013972, A017665-A017712.

[DivisorSigma(9,n): n in [1..20]]; // Bruno Berselli, Apr 10 2013

Table[DivisorSigma[9,n],{n,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *)

PARI
```
a(n)=if(n<1,0,sigma(n,9))
```

[sigma(n,9)for n in range(1,21)] # Zerinvary Lajos, Jun 04 2009

G.f.: Sum_{k>=1} k^9*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003
L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^8)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 06 2017
n^9 + 1 <= a(n) < zeta(9)*n^9. In particular, Grönwall proves lim sup a(n)/n^9 = zeta(9) = A013667. - Charles R Greathouse IV, Dec 27 2021
Sum_{n>=1} a(n)/exp(2*Pi*n) = 1/264 = Bernoulli(10)/20. - Vaclav Kotesovec, May 07 2023
From Amiram Eldar, Oct 29 2023: (Start)
Multiplicative with a(p^e) = (p^(9*e+9)-1)/(p^9-1).
Dirichlet g.f.: zeta(s)*zeta(s-9).
Sum_{k=1..n} a(k) = zeta(10) * n^10 / 10 + O(n^11). (End)

A013956 a(n) = sigma_8(n), the sum of the 8th powers of the divisors of n.

Original entry on oeis.org

1, 257, 6562, 65793, 390626, 1686434, 5764802, 16843009, 43053283, 100390882, 214358882, 431733666, 815730722, 1481554114, 2563287812, 4311810305, 6975757442, 11064693731, 16983563042, 25700456418, 37828630724, 55090232674, 78310985282, 110523825058, 152588281251

Offset: 1

N. J. A. Sloane

If the canonical factorization of n into prime powers is the product of p^e(p) then sigma_k(n) = Product_p ((p^((e(p)+1)*k))-1)/(p^k-1).

Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for sequences related to sigma(n).

Cf. A000203, A001157-A001160, A013667, A013954-A013972, A017665-A017712.

[DivisorSigma(8,n): n in [1..30]]; // Bruno Berselli, Apr 10 2013

Table[DivisorSigma[8,n],{n,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *)

a(n)=sigma(n,8) \\ Charles R Greathouse IV, Apr 28 2011

[sigma(n,8)for n in range(1,21)] # Zerinvary Lajos, Jun 04 2009

G.f.: Sum_{k>=1} k^8*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003
L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^7)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 06 2017
From Amiram Eldar, Oct 29 2023: (Start)
Multiplicative with a(p^e) = (p^(8*e+8)-1)/(p^8-1).
Dirichlet g.f.: zeta(s)*zeta(s-8).
Sum_{k=1..n} a(k) = zeta(9) * n^9 / 9 + O(n^10). (End)

A013961 a(n) = sigma_13(n), the sum of the 13th powers of the divisors of n.

Original entry on oeis.org

1, 8193, 1594324, 67117057, 1220703126, 13062296532, 96889010408, 549822930945, 2541867422653, 10001220711318, 34522712143932, 107006334784468, 302875106592254, 793811662272744, 1946196290656824, 4504149450301441, 9904578032905938, 20825519793796029, 42052983462257060

Offset: 1

N. J. A. Sloane

If the canonical factorization of n into prime powers is the product of p^e(p) then sigma_k(n) = Product_{p prime} ((p^((e(p)+1)*k)) - 1)/(p^k - 1).
Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001
By Fermat's little theorem n^13 == n (mod 13). Hence sigma_13(n) == sigma_(1) (mod 13). In fact, sigma_13(n) == sigma_(1) (mod 2730), where 2730 = 2*3*5*7*13 = the numerator of Bernoulli(12). - Peter Bala, Jan 12 2025

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for sequences related to sigma(n).

Cf. A000203, A001157-A001160, A013672, A013954-A013972, A017665-A017712.

[DivisorSigma(13, n): n in [1..20]]; // Vincenzo Librandi, Sep 10 2016

A013961 := proc(n)
    numtheory[sigma][13](n) ;
end proc: # R. J. Mathar, Sep 21 2017

DivisorSigma[13, Range[30]] (* Vincenzo Librandi, Sep 10 2016 *)

my(N=99, q='q+O('q^N)); Vec(sum(n=1, N, n^13*q^n/(1-q^n))) \\ Altug Alkan, Sep 10 2016

a(n) = sigma(n, 13); \\ Michel Marcus, Sep 10 2016

[sigma(n,13)for n in range(1,16)] # Zerinvary Lajos, Jun 04 2009

G.f.: Sum_{k>=1} k^13*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003
Dirichlet g.f.: zeta(s-13)*zeta(s). - Ilya Gutkovskiy, Sep 10 2016
Empirical: Sum_{n>=1} a(n)/exp(2*Pi*n) = 1/24. - Simon Plouffe, Mar 01 2021
From Amiram Eldar, Oct 29 2023: (Start)
Multiplicative with a(p^e) = (p^(13*e+13)-1)/(p^13-1).
Sum_{k=1..n} a(k) = zeta(14) * n^14 / 14 + O(n^15). (End)

A013958 a(n) = sigma_10(n), the sum of the 10th powers of the divisors of n.

Original entry on oeis.org

1, 1025, 59050, 1049601, 9765626, 60526250, 282475250, 1074791425, 3486843451, 10009766650, 25937424602, 61978939050, 137858491850, 289537131250, 576660215300, 1100586419201, 2015993900450, 3574014537275, 6131066257802, 10250010815226, 16680163512500, 26585860217050

Offset: 1

N. J. A. Sloane

If the canonical factorization of n into prime powers is the product of p^e(p) then sigma_k(n) = Product_p ((p^((e(p)+1)*k))-1)/(p^k-1).

Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for sequences related to sigma(n).

Cf. A000203, A001157-A001160, A013669, A013954-A013972, A017665-A017712.

[DivisorSigma(10,n): n in [1..20]]; // Bruno Berselli, Apr 10 2013

lst={};Do[AppendTo[lst,DivisorSigma[10,n]],{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *)
DivisorSigma[10,Range[20]] (* Harvey P. Dale, Jan 04 2012 *)

a(n)=sigma(n,10) \\ Charles R Greathouse IV, Apr 28 2011

[sigma(n,10)for n in range(1,18)] # Zerinvary Lajos, Jun 04 2009

G.f.: Sum_{k>=1} k^10*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003
L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^9)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 06 2017
From Amiram Eldar, Oct 29 2023: (Start)
Multiplicative with a(p^e) = (p^(10*e+10)-1)/(p^10-1).
Dirichlet g.f.: zeta(s)*zeta(s-10).
Sum_{k=1..n} a(k) = zeta(11) * n^11 / 11 + O(n^12). (End)

A013963 a(n) = sigma_15(n), the sum of the 15th powers of the divisors of n.

Original entry on oeis.org

1, 32769, 14348908, 1073774593, 30517578126, 470199366252, 4747561509944, 35185445863425, 205891146443557, 1000030517610894, 4177248169415652, 15407492847694444, 51185893014090758, 155572843119354936, 437893920912786408, 1152956690052710401, 2862423051509815794

Offset: 1

N. J. A. Sloane

If the canonical factorization of n into prime powers is the product of p^e(p) then sigma_k(n) = Product_p ((p^((e(p)+1)*k))-1)/(p^k-1).

Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for sequences related to sigma(n).

Cf. A000203, A001157-A001160, A013674, A013954-A013972, A017665-A017712.

[DivisorSigma(15, n): n in [1..20]]; // Vincenzo Librandi, Sep 10 2016

DivisorSigma[15, Range[30]] (* Vincenzo Librandi, Sep 10 2016 *)

my(N=99, q='q+O('q^N)); Vec(sum(n=1, N, n^15*q^n/(1-q^n))) \\ Altug Alkan, Sep 10 2016

a(n) = sigma(n, 15); \\ Amiram Eldar, Oct 29 2023

[sigma(n,15)for n in range(1,15)] # Zerinvary Lajos, Jun 04 2009

G.f.: Sum_{k>=1} k^15*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003
Dirichlet g.f.: zeta(s-15)*zeta(s). - Ilya Gutkovskiy, Sep 10 2016
From Amiram Eldar, Oct 29 2023: (Start)
Multiplicative with a(p^e) = (p^(15*e+15)-1)/(p^15-1).
Sum_{k=1..n} a(k) = zeta(16) * n^16 / 16 + O(n^17). (End)

A013969 a(n) = sigma_21(n), the sum of the 21st powers of the divisors of n.

Original entry on oeis.org

1, 2097153, 10460353204, 4398048608257, 476837158203126, 21936961102828212, 558545864083284008, 9223376434903384065, 109418989141972712413, 1000000476837160300278, 7400249944258160101212, 46005141850728850805428, 247064529073450392704414, 1171356134499851307229224

Offset: 1

N. J. A. Sloane

If the canonical factorization of n into prime powers is the product of p^e(p) then sigma_k(n) = Product_p ((p^((e(p)+1)*k))-1)/(p^k-1).

Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001

Seiichi Manyama, Table of n, a(n) for n = 1..10000
Index entries for sequences related to sigma(n).

Cf. A000203, A001157-A001160, A013954-A013972, A017665-A017712.

[DivisorSigma(21,n): n in [1..50]]; // G. C. Greubel, Nov 03 2018

Table[DivisorSigma[21,n],{n,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *)

vector(50, n, sigma(n,21)) \\ G. C. Greubel, Nov 03 2018

[sigma(n,21)for n in range(1,13)] # Zerinvary Lajos, Jun 04 2009

G.f.: Sum_{k>=1} k^21*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003
Sum_{n>=1} a(n)/exp(2*Pi*n) = 77683/552 = Bernoulli(22)/44. - Vaclav Kotesovec, May 07 2023
From Amiram Eldar, Oct 29 2023: (Start)
Multiplicative with a(p^e) = (p^(21*e+21)-1)/(p^21-1).
Dirichlet g.f.: zeta(s)*zeta(s-21).
Sum_{k=1..n} a(k) = zeta(22) * n^22 / 22 + O(n^23). (End)

A013960 a(n) = sigma_12(n), the sum of the 12th powers of the divisors of n.

Original entry on oeis.org

1, 4097, 531442, 16781313, 244140626, 2177317874, 13841287202, 68736258049, 282430067923, 1000244144722, 3138428376722, 8918294543346, 23298085122482, 56707753666594, 129746582562692, 281543712968705, 582622237229762, 1157115988280531, 2213314919066162

Offset: 1

N. J. A. Sloane

If the canonical factorization of n into prime powers is the product of p^e(p) then sigma_k(n) = Product_p ((p^((e(p)+1)*k))-1)/(p^k-1).

Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for sequences related to sigma(n).

Cf. A000203, A001157-A001160, A013671, A013954-A013972, A017665-A017712.

[DivisorSigma(12, n): n in [1..20]]; // Vincenzo Librandi, Sep 10 2016

DivisorSigma[12,Range[20]] (* Harvey P. Dale, Jan 28 2015 *)

my(N=99, q='q+O('q^N)); Vec(sum(n=1, N, n^12*q^n/(1-q^n))) \\ Altug Alkan, Sep 10 2016

a(n) = sigma(n, 12); \\ Amiram Eldar, Oct 29 2023

[sigma(n,12) for n in range(1,17)] # Zerinvary Lajos, Jun 04 2009

G.f.: Sum_{k>=1} k^12*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003
Dirichlet g.f.: zeta(s-12)*zeta(s). - Ilya Gutkovskiy, Sep 10 2016
From Amiram Eldar, Oct 29 2023: (Start)
Multiplicative with a(p^e) = (p^(12*e+12)-1)/(p^12-1).
Sum_{k=1..n} a(k) = zeta(13) * n^13 / 13 + O(n^14). (End)

A013965 a(n) = sigma_17(n), the sum of the 17th powers of the divisors of n.

Original entry on oeis.org

1, 131073, 129140164, 17180000257, 762939453126, 16926788715972, 232630513987208, 2251816993685505, 16677181828806733, 100000762939584198, 505447028499293772, 2218628050709022148, 8650415919381337934, 30491579359845314184, 98526126098761952664

Offset: 1

N. J. A. Sloane

If the canonical factorization of n into prime powers is the product of p^e(p) then sigma_k(n) = Product_p ((p^((e(p)+1)*k))-1)/(p^k-1).

Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for sequences related to sigma(n).

Cf. A000203, A001157-A001160, A013676, A013954-A013972, A017665-A017712.

[DivisorSigma(17, n): n in [1..20]]; // Vincenzo Librandi, Sep 10 2016

DivisorSigma[17,Range[20]] (* Harvey P. Dale, May 30 2013 *)

my(N=99, q='q+O('q^N)); Vec(sum(n=1, N, n^17*q^n/(1-q^n))) \\ Altug Alkan, Sep 10 2016

a(n) = sigma(n, 17); \\ Amiram Eldar, Oct 29 2023

[sigma(n,17)for n in range(1,14)] # Zerinvary Lajos, Jun 04 2009

G.f.: Sum_{k>=1} k^17*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003
Dirichlet g.f.: zeta(s-17)*zeta(s). - Ilya Gutkovskiy, Sep 10 2016
Empirical: Sum_{n>=1} a(n)/exp(2*Pi*n) = 43867/28728, also equals Bernoulli(18)/36. - Simon Plouffe, May 06 2023
From Amiram Eldar, Oct 29 2023: (Start)
Multiplicative with a(p^e) = (p^(17*e+17)-1)/(p^17-1).
Sum_{k=1..n} a(k) = zeta(18) * n^18 / 18 + O(n^19). (End)

A013967 a(n) = sigma_19(n), the sum of the 19th powers of the divisors of n.

Original entry on oeis.org

1, 524289, 1162261468, 274878431233, 19073486328126, 609360902796252, 11398895185373144, 144115462954287105, 1350851718835253557, 10000019073486852414, 61159090448414546292, 319480609006403630044, 1461920290375446110678, 5976315357844100294616

Offset: 1

N. J. A. Sloane

If the canonical factorization of n into prime powers is the product of p^e(p) then sigma_k(n) = Product_p ((p^((e(p)+1)*k))-1)/(p^k-1).

Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001

Seiichi Manyama, Table of n, a(n) for n = 1..10000
Index entries for sequences related to sigma(n).

Cf. A000203, A001157-A001160, A013678, A013954-A013972, A017665-A017712.

[DivisorSigma(19,n): n in [1..50]]; // G. C. Greubel, Nov 03 2018

Table[DivisorSigma[19,n],{n,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *)

vector(50, n, sigma(n,19)) \\ G. C. Greubel, Nov 03 2018

[sigma(n,19)for n in range(1,13)] # Zerinvary Lajos, Jun 04 2009

G.f.: Sum_{k>=1} k^19*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003
From Amiram Eldar, Oct 29 2023: (Start)
Multiplicative with a(p^e) = (p^(19*e+19)-1)/(p^19-1).
Dirichlet g.f.: zeta(s)*zeta(s-19).
Sum_{k=1..n} a(k) = zeta(20) * n^20 / 20 + O(n^21). (End)

cp's OEIS Frontend

A013959 a(n) = sigma_11(n), the sum of the 11th powers of the divisors of n.

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A013957 a(n) = sigma_9(n), the sum of the 9th powers of the divisors of n.

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Magma

Mathematica

PARI

Sage

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A013956 a(n) = sigma_8(n), the sum of the 8th powers of the divisors of n.

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A013961 a(n) = sigma_13(n), the sum of the 13th powers of the divisors of n.

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A013958 a(n) = sigma_10(n), the sum of the 10th powers of the divisors of n.

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A013963 a(n) = sigma_15(n), the sum of the 15th powers of the divisors of n.

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