A133073 a(n) = n^5 + n^3 + n^2.

0, 3, 44, 279, 1104, 3275, 8028, 17199, 33344, 59859, 101100, 162503, 250704, 373659, 540764, 762975, 1052928, 1425059, 1895724, 2483319, 3208400, 4093803, 5164764, 6449039, 7977024, 9781875, 11899628, 14369319, 17233104, 20536379, 24327900, 28659903, 33588224, 39172419, 45475884

Offset

0,2

Comments

Exponents are prime numbers in decreasing order.

Links

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Formula

G.f.: x*(3 + 26*x + 60*x^2 + 30*x^3 + x^4)/(1-x)^6. - R. J. Mathar, Nov 14 2007

a(n) = n^2*(n^3 + n + 1). - Wesley Ivan Hurt, Mar 02 2023

Example

a(7) = 17199 because 7^5 = 16807, 7^3 = 343, 7^2 = 49 and we can write 16807 + 343 + 49 = 17199.

Mathematica

Total[#^{5, 3, 2}]&/@Range[0, 40]  (* Harvey P. Dale, Jan 18 2011 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 3, 44, 279, 1104, 3275}, 35] (* James C. McMahon, Mar 10 2025 *)

Prog

(Magma)[n^5+n^3+n^2: n in [0..50]] // Vincenzo Librandi, Dec 15 2010
(PARI) for(n=0, 50, print1(n^5 + n^3 + n^2, ", ")) \\ G. C. Greubel, Oct 20 2017

Crossrefs

Cf. A000290, A000578, A000584, A011379, A045991, A100019.

Cf. A133070, A133071, A133072.

Sequence in context: A130408 A349646 A296279 * A055539 A046946 A327360

Adjacent sequences: A133070 A133071 A133072 * A133074 A133075 A133076

Keyword

nonn,changed

Author

Omar E. Pol, Nov 01 2007

Extensions

More terms from Vincenzo Librandi, Dec 15 2010

Status

approved