A001015 -id:A001015 - cp's OEIS frontend

A220528 a(n) = n^7 + 7*n + 7^n.

1, 15, 191, 2551, 18813, 94967, 397627, 1647135, 7862009, 45136639, 292475319, 1996813991, 13877119093, 96951759015, 678328486451, 4747732369423, 33233199005169, 232630924325999, 1628414210130607, 11398896079245015, 79792267577612141, 558545865884372695

Offset: 0

Jonathan Vos Post, Dec 15 2012

			a(1) = 1^7 + 7*1 + 7^1 = 15.
a(2) = 2^7 + 7*2 + 7^2 = 191.

Index entries for linear recurrences with constant coefficients, signature (15,-84,252,-462,546,-420,204,-57,7).

Cf. A000420, A001015, A008589, A220425, A220509, A220511, A220703.

Table[n^7 + 7*n + 7^n, {n, 0, 30}] (* T. D. Noe, Dec 17 2012 *)

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

a(n) = A001015(n) + A008589(n) + A000420(n).

G.f.: (55*x^8+546*x^7+8966*x^6+14692*x^5+6726*x^4-694*x^3-50*x^2-1) / ((x-1)^8*(7*x-1)). - Colin Barker, May 09 2013

A240930 a(n) = n^7 - n^6.

Original entry on oeis.org

0, 0, 64, 1458, 12288, 62500, 233280, 705894, 1835008, 4251528, 9000000, 17715610, 32845824, 57921708, 97883968, 159468750, 251658240, 386201104, 578207808, 846825858, 1216000000, 1715322420, 2380977984, 3256789558, 4395368448, 5859375000, 7722894400, 10072932714

Offset: 0

Martin Renner, Aug 03 2014

For n>1 number of 7-digit positive integers in base n.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Cf. A001014, A001015.

Cf. A002378, A045991, A085537, A085538, A085539, A240931, A240932, A240933.

[n^7-n^6 : n in [0..30]]; // Wesley Ivan Hurt, Aug 03 2014

A240930:=n->n^7-n^6: seq(A240930(n), n=0..30); # Wesley Ivan Hurt, Aug 03 2014

Table[n^7 - n^6, {n, 0, 30}] (* Wesley Ivan Hurt, Aug 03 2014 *)
CoefficientList[Series[2 (32*x^2 + 473*x^3 + 1208*x^4 + 718*x^5 + 88*x^6 + x^7)/(x - 1)^8, {x, 0, 30}], x] (* Wesley Ivan Hurt, Aug 03 2014 *)

vector(100, n, (n-1)^7 - (n-1)^6) \\ Derek Orr, Aug 03 2014

a(n) = n^6*(n-1) = n^7 - n^6.
a(n) = A001015(n) - A001014(n).
G.f.: 2*(32*x^2 + 473*x^3 + 1208*x^4 + 718*x^5 + 88*x^6 + x^7)/(x - 1)^8. - Wesley Ivan Hurt, Aug 03 2014
Recurrence: a(n) = 8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)-28*(n-6)+8*a(n-7)-a(n-8). - Wesley Ivan Hurt, Aug 03 2014
Sum_{n>=2} 1/a(n) = 6 - Sum_{k=2..6} zeta(k). - Amiram Eldar, Jul 05 2020

A240931 a(n) = n^8 - n^7.

Original entry on oeis.org

0, 0, 128, 4374, 49152, 312500, 1399680, 4941258, 14680064, 38263752, 90000000, 194871710, 394149888, 752982204, 1370375552, 2392031250, 4026531840, 6565418768, 10407740544, 16089691302, 24320000000, 36021770820, 52381515648, 74906159834, 105488842752, 146484375000

Offset: 0

Martin Renner, Aug 03 2014

For n>1 number of 8-digit positive integers in base n.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Cf. A001015, A001016.

Cf. A002378, A045991, A085537, A085538, A085539, A240930, A240932, A240933.

[n^8-n^7 : n in [0..30]]; // Wesley Ivan Hurt, Aug 09 2014

A240931:=n->n^8-n^7: seq(A240931(n), n=0..30); # Wesley Ivan Hurt, Aug 09 2014

Table[n^8 - n^7, {n, 0, 30}] (* Wesley Ivan Hurt, Aug 09 2014 *)
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{0,0,128,4374,49152,312500,1399680,4941258,14680064},30] (* Harvey P. Dale, Apr 29 2016 *)

vector(100, n, (n-1)^8 - (n-1)^7) \\ Derek Orr, Aug 03 2014

concat([0,0], Vec(-2*x^2*(x^6+183*x^5+2682*x^4+8422*x^3+7197*x^2+1611*x+64) / (x-1)^9 + O(x^100))) \\ Colin Barker, Aug 08 2014

a(n) = n^7*(n-1) = n^8 - n^7.
a(n) = A001016(n) - A001015(n).
G.f.: -2*x^2*(x^6+183*x^5+2682*x^4+8422*x^3+7197*x^2+1611*x+64) / (x-1)^9. - Colin Barker, Aug 08 2014
Sum_{n>=2} 1/a(n) = 7 - Sum_{k=2..7} zeta(k). - Amiram Eldar, Jul 05 2020

A271026 Number of ordered ways to write n as x^7 + y^4 + z^3 + w*(3w+1)/2, where x, y, z are nonnegative integers, and w is an integer.

Original entry on oeis.org

1, 4, 7, 7, 4, 2, 3, 4, 5, 6, 5, 3, 2, 4, 5, 4, 6, 7, 5, 3, 2, 3, 4, 6, 8, 5, 3, 5, 7, 8, 6, 5, 5, 3, 3, 5, 6, 4, 2, 4, 5, 4, 5, 7, 6, 3, 2, 1, 2, 4, 5, 5, 5, 5, 3, 2, 2, 3, 5, 6, 4, 1, 1, 2, 3, 6, 7, 6, 5, 4, 4, 5, 5, 3, 2, 2, 2, 3, 7, 9, 6

Offset: 0

Zhi-Wei Sun, Mar 29 2016

nonn

Conjecture: (i) a(n) > 0 for all n = 0,1,2,..., and a(n) = 1 only for n = 0, 47, 61, 62, 112, 175, 448, 573, 714, 1073, 1175, 1839, 2167, 8043, 13844.
(ii) Any natural number can be written as 3*x^6 + y^4 + z^3 + w*(3w+1)/2, where x, y, z are nonnegative integers and w is an integer.
(iii) For every a = 3, 4, 5, 9, 12, any natural number can be written as a*x^5 + y^4 + z^3 + w*(3w+1)/2, where x, y, z are nonnegative integers and w is an integer. Also, any natural number can be written as x^5 + 2*y^4 + 2*z^3 + w*(3w+1)/2 (or 3*x^5 + 2*y^4 + z^3 + w*(3w+1)/2), where x, y, z are nonnegative integers and w is an integer.
We have verified that a(n) > 0 for n up to 2*10^6.
See also A266968 for a related conjecture.

			a(47) = 1 since 47 = 1^7 + 2^4 + 2^3 + (-4)*(3*(-4)+1)/2.
a(61) = 1 since 61 = 1^7 + 1^4 + 2^3 + (-6)*(3*(-6)+1)/2.
a(62) = 1 since 62 = 0^7 + 0^4 + 3^3 + (-5)*(3*(-5)+1)/2.
a(112) = 1 since 112 = 1^7 + 3^4 + 2^3 + (-4)*(3*(-4)+1)/2.
a(175) = 1 since 175 = 1^7 + 3^4 + 1^3 + (-8)*(3*(-8)+1)/2.
a(448) = 1 since 448 = 2^7 + 4^4 + 4^3 + 0*(3*0+1)/2.
a(573) = 1 since 573 = 1^7 + 4^4 + 6^3 + 8*(3*8+1)/2.
a(714) = 1 since 714 = 2^7 + 4^4 + 0^3 + (-15)*(3*(-15)+1)/2.
a(1073) = 1 since 1073 = 0^7 + 2^4 + 10^3 + 6*(3*6+1)/2.
a(1175) = 1 since 1175 = 0^7 + 5^4 + 5^3 + (-17)*(3*(-17)+1)/2.
a(1839) = 1 since 1839 = 1^7 + 4^4 + 5^3 + 31*(3*31+1)/2.
a(2167) = 1 since 2167 = 1^7 + 5^4 + 11^3 + (-12)*(3*(-12)+1)/2.
a(8043) = 1 since 8043 = 1^7 + 2^4 + 20^3 + 4*(3*4+1)/2.
a(13844) = 1 since 13844 = 3^7 + 2^4 + 21^3 + (-40)*(3*(-40)+1)/2.

Zhi-Wei Sun, Table of n, a(n) for n = 0..10000
Z.-W. Sun, Mixed sums of squares and triangular numbers, Acta Arith. 127(2007), 103-113.
Z.-W. Sun, On universal sums of polygonal numbers, Sci. China Math. 58(2015), 1367-1396.

Cf. A000326, A000578, A000583, A000584, A001015, A001318, A262813, A262815, A262816, A262827, A266968, A270469, A270488, A270516, A270533, A270559, A270566, A270920.

pQ[n_]:=pQ[n]=IntegerQ[Sqrt[24n+1]]
Do[r=0;Do[If[pQ[n-x^7-y^4-z^3],r=r+1],{x,0,n^(1/7)},{y,0,(n-x^7)^(1/4)},{z,0,(n-x^7-y^4)^(1/3)}];Print[n," ",r];Continue,{n,0,80}]

A351341 Least nonnegative integer m such that n = x^4 + y^4 - (z^3 + m^3) for some nonnegative integers x,y,z with z <= m.

Original entry on oeis.org

0, 0, 0, 63, 3, 3, 4, 2, 2, 2, 4, 21, 37, 6, 1, 1, 0, 0, 4, 11, 7, 14, 5, 2, 2, 4, 8, 3, 3, 5, 1, 1, 0, 4, 4, 45, 5, 5, 11, 6, 6, 6, 32, 3, 7, 11, 3, 3, 6, 8, 8, 48, 13, 3, 3, 3, 6, 6, 31, 20, 93, 55, 3, 49, 33, 2, 2, 5, 5, 3, 3, 4, 2, 2, 2, 69, 17, 29, 11, 1, 1, 0, 0, 5, 61, 29, 8, 5, 2, 2, 4, 21, 29, 51, 6, 1, 1, 0, 4, 85, 13

Offset: 0

Zhi-Wei Sun, Feb 08 2022

nonn

Conjecture 1: Let k be 4 or 5. Then each integer can be written as x^k + y^k - (z^3 + w^3) with x,y,z,w nonnegative integers.
Two examples for k = 5: -4 = 58^5 + 76^5 - (775^3 + 1397^3) and 14 = 40^5 + 67^5 - (125^3 + 1132^3).
Conjecture 2: Let k be among 4, 5, 6 and 7. Then any integer can be written as x^k + y^k - (z^2 + w^2) with x,y,z,w nonnegative integers.
Examples for k = 6, 7: 170 = 9^6 + 15^6 - (2114^2 + 2730^2) and 469 = 7^7 + 8^7 - (1001^2 + 1385^2).
Conjecture 3: For any integer k > 3, there are no nonnegative integers x,y,z,w such that x^k + y^k - (z^k + w^k) = 3.
See also another similar conjecture in A351338.

			a(60) = 93 with 60 = 25^4 + 27^4 - (49^3 + 93^3).
a(527) = 527 with 527 = 29^4 + 110^4 - (91^3 + 527^3).
a(2198) = 1704 with 2198 = 85^4 + 304^4 - (1539^3 + 1704^3).
a(4843) = 1965 with 4843 = 142^4 + 338^4 - (1804^3 + 1965^3).

Zhi-Wei Sun, Table of n, a(n) for n = 0..10000

Cf. A000578, A000583, A000584, A001014, A001015, A001481, A004831, A004999, A351306, A351321, A351338.

QQ[n_]:=IntegerQ[n^(1/4)];
tab={};Do[m=0;Label[bb]; k=m^3;Do[If[QQ[n+k+x^3-y^4], tab=Append[tab,m];Goto[aa]],{x,0,m},{y,0,((n+k+x^3)/2)^(1/4)}];m=m+1;Goto[bb];Label[aa],{n, 0, 100}];Print[tab]

A366287 Numbers k such that A163511(k) is a seventh power.

Original entry on oeis.org

0, 64, 129, 259, 519, 1039, 2079, 4159, 8192, 8319, 16385, 16512, 16639, 32771, 33025, 33152, 33279, 65543, 66051, 66305, 66432, 66559, 131087, 132103, 132611, 132865, 132992, 133119, 262175, 264207, 265223, 265731, 265985, 266112, 266239, 524351, 528415, 530447, 531463, 531971, 532225, 532352, 532479, 1048576, 1048703

Offset: 1

Antti Karttunen, Oct 09 2023

nonn

Equivalently, numbers k for which A332214(k), and also A332817(k) are seventh powers.
The sequence is defined inductively as:
 (a) it contains 0 and 64,
   and
 (b) for any nonzero term a(n), (2*a(n)) + 1 and 128*a(n) are also included as terms.
When iterating n -> 2n+1 mod 127, starting from 64 we get 64, 2, 5, 11, 23, 47, 95, and then cycle starts again from 64 (see A153893), while on the other hand, x^7 mod 127 obtains values: 0, 1, 19, 20, 22, 24, 28, 37, 52, 59, 68, 75, 90, 99, 103, 105, 107, 108, 126. These sets have no terms in common, therefore there are no seventh powers in this sequence after the initial 0.

Positions of multiples of 7 in A365805.
Sequence A243071(n^7), n >= 1, sorted into ascending order.
Cf. A001015, A153893, A163511, A332214, A332817.
Cf. A365801, A365802, A365808, A366391.

A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
isA366287(n) = ispower(A163511(n),7);

isA366287(n) = if(n<=64, !(n%64), if(n%2, isA366287((n-1)/2), if(n%128, 0, isA366287(n>>7))));

A084549 Numbers k that have primitive roots less than k that are nonnegative perfect seventh powers.

Original entry on oeis.org

2, 131, 139, 149, 163, 169, 173, 179, 181, 227, 243, 269, 293, 317, 347, 349, 361, 373, 389, 419, 443, 461, 467, 509, 523, 541, 557, 563, 587, 613, 619, 625, 653, 661, 677, 709, 729, 773, 787, 797, 821, 829, 853, 859, 877, 907, 941, 947, 1019, 1061, 1091, 1109

Offset: 1

Hauke Worpel (hw1(AT)email.com), May 30 2003

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A001015, A084547, A084548, A084550.

q[n_] := Intersection[PrimitiveRootList[n], Range[Floor@Surd[n, 7]]^7] != {}; Select[Range[1000], q] (* Amiram Eldar, Oct 07 2021 *)

a(1) inserted and more terms added by Amiram Eldar, Oct 07 2021

A168663 a(n) = n^7*(n^6 + 1)/2.

Original entry on oeis.org

0, 1, 4160, 798255, 33562624, 610390625, 6530486976, 48444916975, 274878955520, 1270935305649, 5000005000000, 17261365815551, 53496620605440, 151437584670385, 396857439333824, 973097619609375, 2251799947902976

Offset: 0

N. J. A. Sloane, Dec 11 2009

Number of unoriented rows of length 13 using up to n colors. For a(0)=0, there are no rows using no colors. For a(1)=1, there is one row using that one color for all positions. For a(2)=4160, there are 2^13=8192 oriented arrangements of two colors. Of these, 2^7=128 are achiral. That leaves (8192-128)/2=4032 chiral pairs. Adding achiral and chiral, we get 4160. - Robert A. Russell, Nov 13 2018

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).

Row 13 of A277504.

Cf. A010801 (oriented), A001015 (achiral).

[n^7*(n^6+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 28 2011

Table[n^7(n^6+1)/2,{n,0,20}] (* Harvey P. Dale, Jan 20 2013 *)

a(n)=n^7*(n^6+1)/2 \\ Charles R Greathouse IV, Jul 28 2016

From G. C. Greubel, Jul 28 2016: (Start)
G.f.: x*(1 + 4146*x + 740106*x^2 + 22765250*x^3 + 211641855*x^4 + 752814348*x^5 + 1137578988*x^6 + 752814348*x^7 + 211641855*x^8 + 22765250*x^9 + 740106*x^10 + 4146*x^11 + x^12)/(1 - x)^14.
E.g.f.: (1/2)*x*(2 + 4158*x + 261926*x^2 + 2532880*x^3 + 7508641*x^4 + 9321333*x^5 + 5715425*x^6 + 1899612*x^7 + 359502*x^8 + 39325*x^9 + 2431*x^10 + 78*x^11 + x^12)*exp(x). (End)
From Robert A. Russell, Nov 13 2018: (Start)
a(n) = (A010801(n) + A001015(n)) / 2 = (n^13 + n^7) / 2.
G.f.: (Sum_{j=1..13} S2(13,j)*j!*x^j/(1-x)^(j+1) + Sum_{j=1..7} S2(7,j)*j!*x^j/(1-x)^(j+1)) / 2, where S2 is the Stirling subset number A008277.
G.f.: x*Sum_{k=0..12} A145882(13,k) * x^k / (1-x)^14.
E.g.f.: (Sum_{k=1..13} S2(13,k)*x^k + Sum_{k=1..7} S2(7,k)*x^k) * exp(x) / 2, where S2 is the Stirling subset number A008277.
For n>13, a(n) = Sum_{j=1..14} -binomial(j-15,j) * a(n-j). (End)

A168664 a(n) = n^7*(n^7 + 1)/2.

Original entry on oeis.org

0, 1, 8256, 2392578, 134225920, 3051796875, 39182222016, 339111948196, 2199024304128, 11438398618965, 50000005000000, 189874926535206, 641959250190336, 1968688224223903, 5556003465485760, 14596463098125000, 36028797153181696, 84188913484869801

Offset: 0

N. J. A. Sloane, Dec 11 2009

Number of unoriented rows of length 14 using up to n colors. For a(0)=0, there are no rows using no colors. For a(1)=1, there is one row using that one color for all positions. For a(2)=8256, there are 2^14=16384 oriented arrangements of two colors. Of these, 2^7=128 are achiral. That leaves (16384-128)/2=8128 chiral pairs. Adding achiral and chiral, we get 8256. - Robert A. Russell, Nov 13 2018

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005, -3003,1365,-455,105,-15,1).

Cf. A001015 (Seventh Powers: n^7), A000217 (Triangular Numbers).
Row 14 of A277504.
Cf. A010802 (oriented), A001015 (achiral).

List([0..30], n -> n^7*(1 + n^7)/2); # G. C. Greubel, Nov 15 2018

[n^7*(n^7+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 28 2011

A168664:=n->n^7*(n^7+1)/2: seq(A168664(n), n=0..20); # Wesley Ivan Hurt, Oct 30 2014

f[n_]:=Module[{c=n^7},c (c+1)/2]; f/@Range[0,30] (* Harvey P. Dale, Mar 19 2011 *)

a(n)=n^7*(n^7+1)/2 \\ Charles R Greathouse IV, Jul 28 2016

[n^7*(1 + n^7)/2 for n in range(40)] # G. C. Greubel, Nov 15 2018

From Wesley Ivan Hurt, Oct 30 2014: (Start)
G.f.: (x + 8241*x^2 + 2268843*x^3 + 99203675*x^4 + 1285873650*x^5 + 6421633938*x^6 + 13985577438*x^7 + 13985598654*x^8 + 6421628925*x^9 + 1285868525*x^10 + 99207111*x^11 + 2268471*x^12 + 8128*x^13)/(1 - x)^15.
a(n) = 15*a(n-1) - 105*a(n-2) + 455*a(n-3) - 1365*a(n-4) + 3003*a(n-5) - 5005*a(n-6) + 6435*a(n-7) - 6435*a(n-8) + 5005*a(n-9) - 3003*a(n-10) + 1365*a(n-11) - 455*a(n-12) + 105*a(n-13) - 15*a(n-14) + a(n-15).
a(n) = n^7*(n^7 + 1)/2 = A000217(A001015(n)). (End)
From Robert A. Russell, Nov 13 2018: (Start)
a(n) = (A010802(n) + A001015(n)) / 2 = (n^14 + n^7) / 2.
G.f.: (Sum_{j=1..14} S2(14,j)*j!*x^j/(1-x)^(j+1) + Sum_{j=1..7} S2(7,j)*j!*x^j/(1-x)^(j+1)) / 2, where S2 is the Stirling subset number A008277.
G.f.: x*Sum_{k=0..13} A145882(14,k) * x^k / (1-x)^15.
E.g.f.: (Sum_{k=1..14} S2(14,k)*x^k + Sum_{k=1..7} S2(7,k)*x^k) * exp(x) / 2, where S2 is the Stirling subset number A008277.
For n>14, a(n) = Sum_{j=1..15} -binomial(j-16,j) * a(n-j). (End)
E.g.f.: x*(2+8254*x +789271*x^2 +10392095*x^3 +40075175*x^4 +63436394*x^5 +49329281*x^6 +20912320*x^7 +5135130*x^8 +752752*x^9 + 66066*x^10 +3367*x^11 +91*x^12 +x^13)*exp(x)/2. - G. C. Greubel, Nov 15 2018

A283018 Primes which are the sum of three positive 7th powers.

Original entry on oeis.org

3, 257, 82499, 823799, 1119863, 2099467, 4782971, 5063033, 5608699, 6880249, 7160057, 10018571, 10078253, 10094509, 10279937, 10389481, 10823671, 19503683, 20002187, 20388839, 24782969, 31584323, 35850379, 36189869, 37931147, 50614777, 57416131, 62765029, 64845797, 68355029, 71663617, 73028453

Offset: 1

Ilya Gutkovskiy, Feb 26 2017

nonn

Primes of form x^7 + y^7 + z^7 where x, y, z > 0.

			3 = 1^7 + 1^7 + 1^7;
257 = 1^7 + 2^7 + 2^7;
82499 = 3^7 + 3^7 + 5^7, etc.

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

Cf. A001015, A003370, A007490, A085317, A085318, A085319, A283017, A283019.

N:= 10^9: # to get all terms <= N
Res:= {}:
for x from 1 to floor(N^(1/7)) do
  for y from 1 to min(x, floor((N-x^7)^(1/7))) do
    for z from 1 to min(y, floor((N-x^7-y^7)^(1/7))) do
      p:= x^7 + y^7 + z^7;
      if isprime(p) then Res:= Res union {p} fi
od od od:
sort(convert(Res,list)); # Robert Israel, Feb 26 2017

nn = 14; Select[Union[Plus @@@ (Tuples[Range[nn], {3}]^7)], # <= nn^7 && PrimeQ[#] &]

list(lim)=my(v=List(),x7,y7,t,p); for(x=1,sqrtnint(lim\3,7), x7=x^7; for(y=x,sqrtnint((lim-x7)\2,7), y7=y^7; t=x7+y7; forstep(z=y+(x+1)%2,sqrtnint((lim-t)\1,7),2, if(isprime(p=t+z^7), listput(v,p))))); Set(v) \\ Charles R Greathouse IV, Feb 27 2017

cp's OEIS Frontend

A220528 a(n) = n^7 + 7*n + 7^n.

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A240930 a(n) = n^7 - n^6.

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A240931 a(n) = n^8 - n^7.

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PARI

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A271026 Number of ordered ways to write n as x^7 + y^4 + z^3 + w*(3w+1)/2, where x, y, z are nonnegative integers, and w is an integer.

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A351341 Least nonnegative integer m such that n = x^4 + y^4 - (z^3 + m^3) for some nonnegative integers x,y,z with z <= m.

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Mathematica

A366287 Numbers k such that A163511(k) is a seventh power.

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PARI

PARI

A084549 Numbers k that have primitive roots less than k that are nonnegative perfect seventh powers.

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Extensions

A168663 a(n) = n^7*(n^6 + 1)/2.

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