A000584 -id:A000584 - cp's OEIS frontend

A001160 sigma_5(n), the sum of the 5th powers of the divisors of n.

1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158, 161052, 257908, 371294, 554664, 762744, 1082401, 1419858, 1956669, 2476100, 3304182, 4101152, 5314716, 6436344, 8253300, 9768751, 12252702, 14408200, 17766056, 20511150

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
Empirical: Sum_{n>=1} a(n)/exp(2*Pi*n) = 1/504. - Simon Plouffe, Mar 01 2021

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math.Series 55, Tenth Printing, 1972, p. 827.
G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work, AMS Chelsea Publishing, Providence, Rhode Island, 2002, p. 166.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Zagier, Don. "Elliptic modular forms and their applications." The 1-2-3 of modular forms. Springer Berlin Heidelberg, 2008. 1-103. See p. 17, G_6(z).

T. D. Noe, Table of n, a(n) for n = 1..10000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math.Series 55, Tenth Printing, 1972, p. 827.
Index entries for sequences related to sigma(n)

Cf. A000005, A000203, A001157, A001158, A001159, A013973, A000584 (Mobius transform), A178448 (Dirichlet inverse)

[DivisorSigma(5,n): n in [1..30]]; // Bruno Berselli, Apr 10 2013

A001160 := proc(n)
    numtheory[sigma][5](n);
end proc:
seq(A001160(n),n=1..30) ; # R. J. Mathar, Jan 31 2017

lst={};Do[AppendTo[lst,DivisorSigma[5,n]],{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *)
DivisorSigma[5,Range[30]] (* Harvey P. Dale, Nov 11 2013 *)

a(n)=sigma(n,5) \\ Charles R Greathouse IV, Apr 28 2011

[sigma(n, 5) for n in range(1, 30)]  # Zerinvary Lajos, Jun 04 2009

Multiplicative with a(p^e) = (p^(5e+5)-1)/(p^5-1). - David W. Wilson, Aug 01 2001
G.f.: sum(k>=1, k^5*x^k/(1-x^k)). - Benoit Cloitre, Apr 21 2003
Dirichlet g.f.: zeta(s)*zeta(s-5). - R. J. Mathar, Mar 06 2011
G.f. also (1 - E_6(q))/540, with the g.f. E_6 of A013973. See Hardy p. 166, (10.5.7) with R = E_6. - Wolfdieter Lang, Jan 31 2017
L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^4)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 06 2017
a(n) = Sum_{1 <= i, j, k, l, m <= n} tau(gcd(i, j, k, l, m, n)) = Sum_{d divides n} tau(d) * J_5(n/d), where the divisor function tau(n) = A000005(n) and the Jordan totient function J_5(n) = A059378(n). - Peter Bala, Jan 22 2024

A268335 Exponentially odd numbers.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 8, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 24, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 46, 47, 51, 53, 54, 55, 56, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 88, 89, 91, 93, 94, 95, 96, 97

Offset: 1

Vladimir Shevelev, Feb 01 2016

nonn

The sequence is formed by 1 and the numbers whose prime power factorization contains only odd exponents.
The density of the sequence is the constant given by A065463.
Except for the first term the same as A002035. - R. J. Mathar, Feb 07 2016
Also numbers k all of whose divisors are bi-unitary divisors (i.e., A286324(k) = A000005(k)). - Amiram Eldar, Dec 19 2018
The term "exponentially odd integers" was apparently coined by Cohen (1960). These numbers were also called "unitarily 2-free", or "2-skew", by Cohen (1961). - Amiram Eldar, Jan 22 2024

Peter J. C. Moses, Table of n, a(n) for n = 1..2000
Eckford Cohen, Arithmetical functions associated with the unitary divisors of an integer, Mathematische Zeitschrift, Vol. 74 (1960), pp. 66-80.
Eckford Cohen, Some sets of integers related to the k-free integers, Acta Sci. Math. (Szeged), Vol. 22, No. 3-4 (1961), pp. 223-233.
Vladimir Shevelev, Exponentially S-numbers, arXiv:1510.05914 [math.NT], 2015.
Vladimir Shevelev, Set of all densities of exponentially S-numbers, arXiv preprint arXiv:1511.03860 [math.NT], 2015.
Vladimir Shevelev, S-exponential numbers, Acta Arithmetica, Vol. 175(2016), 385-395.
D. Suryanarayana and R. Sita Rama Chandra Rao, Distribution of unitarily k-free integers, Journal of the Australian Mathematical Society, Vol. 20 , No. 2 (1975), pp. 129-141.

Cf. A002035, A209061, A138302, A197680, A000578, A000584, A001014, A001017, A008456, A010803, A010805, A010806, A010808, A010811, A010812, A001221, A124010.

Select[Range@ 100, AllTrue[Last /@ FactorInteger@ #, OddQ] &] (* Version 10, or *)
Select[Range@ 100, Times @@ Boole[OddQ /@ Last /@ FactorInteger@ #] == 1 &] (* Michael De Vlieger, Feb 02 2016 *)

isok(n)=my(f = factor(n)); for (k=1, #f~, if (!(f[k,2] % 2), return (0))); 1; \\ Michel Marcus, Feb 02 2016

from itertools import count, islice
from sympy import factorint
def A268335_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:all(e&1 for e in factorint(n).values()),count(max(startvalue,1)))
A268335_list = list(islice(A268335_gen(),20)) # Chai Wah Wu, Jun 22 2023

Sum_{a(n)<=x} 1 = C*x + O(sqrt(x)*log x*e^(c*sqrt(log x)/(log(log x))), where c = 4*sqrt(2.4/log 2) = 7.44308... and C = Product_{prime p} (1 - 1/p*(p + 1)) = 0.7044422009991... (A065463).

Sum_{n>=1} 1/a(n)^s = zeta(2*s) * Product_{p prime} (1 + 1/p^s - 1/p^(2*s)), s>1. - Amiram Eldar, Sep 26 2023

A001015 Seventh powers: a(n) = n^7.

Original entry on oeis.org

0, 1, 128, 2187, 16384, 78125, 279936, 823543, 2097152, 4782969, 10000000, 19487171, 35831808, 62748517, 105413504, 170859375, 268435456, 410338673, 612220032, 893871739, 1280000000, 1801088541, 2494357888, 3404825447, 4586471424, 6103515625, 8031810176

Offset: 0

N. J. A. Sloane

For n>0, (a(3*n-1)^7-a(2*n-1)^7-a(n)^7)/(7*(3*n-1)*(2*n-1)*n) = (2*A001106(n)+1)^2 (see Barisien reference, problem 173). - Bruno Berselli, Feb 01 2011

Number of the form a(n) + a(n+1) + ... + a(n+k) is never prime for all n, k>=0. This could be proved by the method indicated in the comment in A256581. - Vladimir Shevelev and Peter J. C. Moses, Apr 04 2015

E.-N. Barisien, Supplemento al Periodico di Matematica, Raffaello Giusti Editore (Livorno), July 1913, p. 135 (Problem 173).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 0..1000
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Cf. A000584 (5th powers), A013665 (zeta(7)), A275710 (eta(7)), A300785.

Cf. A003369 - A003379 (sums of 2, ..., 12 positive seventh powers).

A001015:=z*(1191*z^4+120*z^5+1191*z^2+2416*z^3+120*z+z^6+1)/(z-1)^8; # Simon Plouffe in his 1992 dissertation; offset corrected by M. F. Hasler, Feb 01 2011

Table[n^7, {n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Apr 15 2011 *)

makelist(n^7,n,0,20); /* Martin Ettl, Jan 15 2013 */

A001015(n)=n^7 \\ Charles R Greathouse IV, Sep 24 2015

A001015 = lambda n: n**7 # M. F. Hasler, Jul 03 2025

Multiplicative with a(p^e) = p^(7e). - David W. Wilson, Aug 01 2001
Totally multiplicative sequence with a(p) = p^7 for primes p. - Jaroslav Krizek, Nov 01 2009
a(n) = 7*a(n-1) - 21* a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) + 5040. - Ant King, Sep 24 2013
a(n) = n + Sum_{j=0..n-1}{k=1..6}binomial(7,k)*j^(7-k). - Patrick J. McNab, Mar 28 2016
G.f.: x*(1+120*x+1191*x^2+2416*x^3+1191*x^4+120*x^5+x^6)/(1-x)^8. See the Maple program. - Wolfdieter Lang, Oct 14 2016
From Kolosov Petro, Oct 22 2018: (Start)
a(n) = Sum_{k=1..n} A300785(n,k).
a(n) = Sum_{k=0..n-1} A300785(n,k). (End)
From Amiram Eldar, Oct 08 2020: (Start)
Sum_{n>=1} 1/a(n) = zeta(7) (A013665).
Sum_{n>=1} (-1)^(n+1)/a(n) = 63*zeta(7)/64 (A275710). (End)

More terms from James Sellers, Sep 19 2000

A000539 Sum of 5th powers: 0^5 + 1^5 + 2^5 + ... + n^5.

Original entry on oeis.org

0, 1, 33, 276, 1300, 4425, 12201, 29008, 61776, 120825, 220825, 381876, 630708, 1002001, 1539825, 2299200, 3347776, 4767633, 6657201, 9133300, 12333300, 16417401, 21571033, 28007376, 35970000, 45735625, 57617001, 71965908, 89176276, 109687425, 133987425, 162616576

Offset: 0

N. J. A. Sloane

This sequence is related to A000538 by a(n) = n*A000538(n) - Sum_{i=0..n-1} A000538(i). - Bruno Berselli, Apr 26 2010

See comment in A008292 for a formula for r-th successive summation of Sum_{k=1..n} k^j. - Gary Detlefs, Jan 02 2014

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 813.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 155.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1991, p. 275.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 0..1000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Bruno Berselli, A description of the transform in Comments lines: website Matem@ticamente (in Italian).
Feihu Liu, Guoce Xin, and Chen Zhang, Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS, arXiv:2412.18744 [math.CO], 2024. See p. 13.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Eric Weisstein's World of Mathematics, Faulhaber's Formula
Wikipedia, Faulhaber's formula
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Partial sums of A000584. Row 5 of array A103438.

Cf. A000217, A000537, A000538, A006542, A008292, A059378, A101092.

[n^2*(n+1)^2*(2*n^2+2*n-1)/12: n in [0..30]]; // Vincenzo Librandi, Apr 04 2015

A000539:=-(1+26*z+66*z**2+26*z**3+z**4)/(z-1)**7; # Simon Plouffe in his 1992 dissertation
a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=a[n-1]+n^5 od: seq(a[n], n=0..30); # Zerinvary Lajos, Feb 22 2008
a:=n->sum(j^5,j=0..n): seq(a(n), n=0..30); # Zerinvary Lajos, Jun 05 2008

Accumulate[Range[0, 40]^5]
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 1, 33, 276, 1300, 4425, 12201}, 41] (* Jean-François Alcover, Feb 09 2016 *)

A000539(n):=n^2*(n+1)^2*(2*n^2+2*n-1)/12$ makelist(A000539(n),n,0,30); /* Martin Ettl, Nov 12 2012 */

a(n)=n^2*(n+1)^2*(2*n^2+2*n-1)/12 \\ Charles R Greathouse IV, Jul 15 2011

concat(0, Vec(x*(1+26*x+66*x^2+26*x^3+x^4)/(1-x)^7 + O(x^100))) \\ Altug Alkan, Dec 07 2015

A000539_list, m = [0], [120, -240, 150, -30, 1, 0, 0]
for _ in range(10**2):
    for i in range(6):
        m[i+1] += m[i]
    A000539_list.append(m[-1]) # Chai Wah Wu, Nov 05 2014

def A000539(n): return n**2*(n**2*(n*(n+3<<1)+5)-1)//12 # Chai Wah Wu, Oct 03 2024

a(n) = n^2*(n+1)^2*(2*n^2+2*n-1)/12.
a(n) = sqrt(Sum_{j=1..n}Sum_{i=1..n}(i*j)^5). - Alexander Adamchuk, Oct 26 2004
a(n) = Sum_{i = 1..n} J_5(i)*floor(n/i), where J_5 is A059378. - Enrique Pérez Herrero, Feb 26 2012
a(n) = 6*a(n-1) - 15* a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) + 120. - Ant King, Sep 23 2013
a(n) = 120*C(n+3,6) + 30*C(n+2,4) + C(n+1,2) (Knuth). - Gary Detlefs, Jan 02 2014
a(n) = -Sum_{j=1..5} j*Stirling1(n+1,n+1-j)*Stirling2(n+5-j,n). - Mircea Merca, Jan 25 2014
Sum_{n>=1} 1/a(n) = 60 - 4*Pi^2 + 8*sqrt(3)*Pi * tan(sqrt(3)*Pi/2). - Vaclav Kotesovec, Feb 13 2015
a(n) = (n + 1)^2*n^2*(n + 1/2 + sqrt(3/4))*(n + 1/2 - sqrt(3/4))/6. See the Graham et al. reference, p. 275. - Wolfdieter Lang, Apr 02 2015
G.f.: x*(1+26*x+66*x^2+26*x^3+x^4)/(1-x)^7. - Robert Israel, Dec 07 2015
a(n) = (4/3)*A000217(n)^3 - (1/3)*A000217(n)^2. - Michael Raney, Feb 19 2016
a(n) = (binomial(n+1,4) + 6*binomial(n+2,4) + binomial(n+3,4))*(binomial(n+2,3) - binomial(n+1,3)). - Tony Foster III, Oct 21 2018
a(n) = 24*A006542(n+2) + A000537(n). - Yasser Arath Chavez Reyes, May 04 2024
E.g.f.: exp(x)*x*(12 + 186*x + 360*x^2 + 195*x^3 + 36*x^4 + 2*x^5)/12. - Stefano Spezia, May 04 2024

A003347 Numbers that are the sum of 2 positive 5th powers.

Original entry on oeis.org

2, 33, 64, 244, 275, 486, 1025, 1056, 1267, 2048, 3126, 3157, 3368, 4149, 6250, 7777, 7808, 8019, 8800, 10901, 15552, 16808, 16839, 17050, 17831, 19932, 24583, 32769, 32800, 33011, 33614, 33792, 35893, 40544, 49575, 59050, 59081, 59292, 60073, 62174, 65536, 66825, 75856

Offset: 1

N. J. A. Sloane

nonn

			From _David A. Corneth_, Aug 03 2020: (Start)
917552689 is in the sequence as 917552689 = 17^5 + 62^5.
2557575000 is in the sequence as 2557575000 = 45^5 + 75^5.
5828050944 is in the sequence as 5828050944 = 56^5 + 88^5. (End)

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
Samuel S. Wagstaff, Jr., Equal Sums of Two Distinct Like Powers, J. Int. Seq., Vol. 25 (2022), Article 22.3.1.

Cf. A000584, A003336, A003348, A003358, A088703.

With[{k = 5}, Union@ Map[(#[[1]]^k + #[[2]]^k) &, Tuples[Range[9], {2}]]] (* Michael De Vlieger, Sep 09 2022, after Harvey P. Dale at A004999  *)

A003350 Numbers that are the sum of 5 positive 5th powers.

Original entry on oeis.org

5, 36, 67, 98, 129, 160, 247, 278, 309, 340, 371, 489, 520, 551, 582, 731, 762, 793, 973, 1004, 1028, 1059, 1090, 1121, 1152, 1215, 1270, 1301, 1332, 1363, 1512, 1543, 1574, 1754, 1785, 1996, 2051, 2082, 2113, 2144, 2293, 2324, 2355, 2535, 2566, 2777, 3074, 3105, 3129

Offset: 1

N. J. A. Sloane

			From _David A. Corneth_, Aug 03 2020: (Start)
122490 is in the sequence as 122490 = 3^5 + 4^5 + 5^5 + 9^5 + 9^5.
251124 is in the sequence as 251124 = 1^5 + 3^5 + 4^5 + 4^5 + 12^5.
349858 is in the sequence as 349858 = 1^5 + 1^5 + 4^5 + 10^5 + 12^5. (End)

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Cf. A000584, A003349, A003351, A003339, A342685, A344643

Column k=5 of A336725.

f[upto_]:=Module[{max=Floor[Power[upto, (5)^-1]],tp},tp=Union[ Total/@ (Tuples[ Range[max],{5}]^5)]; Select[tp,#<=upto&]]; f[2100]  (* Harvey P. Dale, Mar 22 2011 *)

A003349 Numbers that are the sum of 4 positive 5th powers.

Original entry on oeis.org

4, 35, 66, 97, 128, 246, 277, 308, 339, 488, 519, 550, 730, 761, 972, 1027, 1058, 1089, 1120, 1269, 1300, 1331, 1511, 1542, 1753, 2050, 2081, 2112, 2292, 2323, 2534, 3073, 3104, 3128, 3159, 3190, 3221, 3315, 3370, 3401, 3432, 3612, 3643, 3854, 4096, 4151, 4182, 4213

Offset: 1

N. J. A. Sloane

			From _David A. Corneth_, Aug 03 2020: (Start)
670593 is in the sequence as 670593 = 1^5 + 8^5 + 10^5 + 14^5.
862512 is in the sequence as 862512 = 7^5 + 9^5 + 12^5 + 14^5.
1892695 is in the sequence as 1892695 = 1^5 + 1^5 + 5^5 + 18^5. (End)

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Cf. A000584, A003338, A003348, A003350, A344642, A344644.

f@n_:= Select[Range@n,IntegerPartitions[#,{4},Range@(n^(1/5))^5] != {} &]; f@10000 (* Hans Rudolf Widmer, Dec 04 2022 *)

Incorrect program removed by David A. Corneth, Aug 03 2020

A003351 Numbers that are the sum of 6 positive 5th powers.

Original entry on oeis.org

6, 37, 68, 99, 130, 161, 192, 248, 279, 310, 341, 372, 403, 490, 521, 552, 583, 614, 732, 763, 794, 825, 974, 1005, 1029, 1036, 1060, 1091, 1122, 1153, 1184, 1216, 1247, 1271, 1302, 1333, 1364, 1395, 1458, 1513, 1544, 1575, 1606, 1755, 1786, 1817, 1997, 2028, 2052

Offset: 1

N. J. A. Sloane

			From _David A. Corneth_, Aug 03 2020: (Start)
90185 is in the sequence as 90185 = 2^5 + 6^5 + 6^5 + 6^5 + 6^5 + 9^5.
104636 is in the sequence as 104636 = 1^5 + 3^5 + 3^5 + 4^5 + 5^5 + 10^5.
151173 is in the sequence as 151173 = 2^5 + 2^5 + 3^5 + 8^5 + 9^5 + 9^5. (End)

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Cf. A000584, A003340, A003350, A003352, A345507, A346356.

A003352 Numbers that are the sum of 7 positive 5th powers.

Original entry on oeis.org

7, 38, 69, 100, 131, 162, 193, 224, 249, 280, 311, 342, 373, 404, 435, 491, 522, 553, 584, 615, 646, 733, 764, 795, 826, 857, 975, 1006, 1030, 1037, 1061, 1068, 1092, 1123, 1154, 1185, 1216, 1217, 1248, 1272

Offset: 1

N. J. A. Sloane

			From _David A. Corneth_, Aug 03 2020: (Start)
41940 is in the sequence as 41940 = 2^5 + 2^5 + 3^5 + 3^5 + 6^5 + 7^5 + 7^5.
65614 is in the sequence as 65614 = 1^5 + 3^5 + 3^5 + 6^5 + 6^5 + 7^5 + 8^5.
96845 is in the sequence as 96845 = 1^5 + 2^5 + 4^5 + 5^5 + 7^5 + 7^5 + 9^5. (End)

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Cf. A000584, A003341, A003351, A003353, A345605, A346278.

Incorrect program removed by David A. Corneth, Aug 03 2020

A003353 Numbers that are the sum of 8 positive 5th powers.

Original entry on oeis.org

8, 39, 70, 101, 132, 163, 194, 225, 250, 256, 281, 312, 343, 374, 405, 436, 467, 492, 523, 554, 585, 616, 647, 678, 734, 765, 796, 827, 858, 889, 976, 1007, 1031, 1038, 1062, 1069, 1093, 1100, 1124, 1155, 1186, 1217, 1218, 1248, 1249, 1273, 1280, 1304, 1311, 1335, 1366

Offset: 1

N. J. A. Sloane

			From _David A. Corneth_, Aug 03 2020: (Start)
32373 is in the sequence as 32373 = 1^5 + 1^5 + 3^5 + 4^5 + 6^5 + 6^5 + 6^5 + 6^5.
42605 is in the sequence as 42605 = 3^5 + 3^5 + 3^5 + 3^5 + 3^5 + 6^5 + 7^5 + 7^5.
58030 is in the sequence as 58030 = 2^5 + 2^5 + 4^5 + 6^5 + 6^5 + 6^5 + 7^5 + 7^5. (End)

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Cf. A000584, A003342, A003352, A003354, A345610, A346326.

cp's OEIS Frontend

A001160 sigma_5(n), the sum of the 5th powers of the divisors of n.

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A268335 Exponentially odd numbers.

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A001015 Seventh powers: a(n) = n^7.

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A000539 Sum of 5th powers: 0^5 + 1^5 + 2^5 + ... + n^5.

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PARI

PARI

Python

Python

Formula

A003347 Numbers that are the sum of 2 positive 5th powers.

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Mathematica

A003350 Numbers that are the sum of 5 positive 5th powers.

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Author

Keywords

Examples

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Programs

Mathematica