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A269527 a(n) = n^20 + n^15 + n^10 + n^5 + 1. 1
1, 5, 1082401, 3501192601, 1100586419201, 95397958987501, 3656628685521505, 79797014141614001, 1152956690052710401, 12157871353675866901, 100001000010000100001, 672754172206667010505, 3833775399530967321601, 19005014960911672392701, 83668410993669614565601 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = Phi_25(n) where Phi_k(x) is the k-th cyclotomic polynomial.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Eric Weisstein's World of Mathematics, Cyclotomic Polynomial

Index to values of cyclotomic polynomials of integer argument

Index entries for linear recurrences with constant coefficients, signature (21, -210, 1330, -5985, 20349, -54264, 116280, -203490, 293930, -352716, 352716, -293930, 203490, -116280, 54264, -20349, 5985, -1330, 210, -21, 1).

FORMULA

G.f.: (1 - 16*x + 1082506*x^2 + 3478461900*x^3 + 1027288678125*x^4 + 73019455046736*x^5 + 1879744586779368*x^6 + 21598535807594352*x^7 + 124747954270666290*x^8 + 388588494914595280*x^9 + 679562623971548876*x^10 + 679561811581541512*x^11 + 388588026599578578*x^12 + 124748409900243120*x^13 + 21598656801538440*x^14 + 1879672759361136*x^15 + 72997577685261*x^16 + 1025730080064*x^17 + 3451141690*x^18 + 1016780*x^19 + x^20)/(1 - x)^21.

Sum_{n>=0} 1/a(n) = 1.200000924158557891...

MAPLE

a:= n-> add(n^(5*j), j=0..4):

seq(a(n), n=0..18);  # Alois P. Heinz, Apr 24 2019

MATHEMATICA

Table[Cyclotomic[25, n], {n, 0, 12}]

Join[{1}, Table[Total[n^(5*Range[0, 4])], {n, 20}]] (* Harvey P. Dale, Sep 01 2016 *)

PROG

(MAGMA) [n^20+n^15+n^10+n^5+1: n in [0..20]]; // Vincenzo Librandi, Feb 29 2016

(PARI) a(n) = polcyclo(25, n); \\ Michel Marcus, Feb 29 2016

(Sage) [sum(n^(5*j) for j in (0..4)) for n in (0..20)] # G. C. Greubel, Apr 24 2019

(GAP) List([0..20], n-> Sum([0..4], j-> n^(5*j))) # G. C. Greubel, Apr 24 2019

CROSSREFS

Cf. similar sequences of the type Phi_k(n) listed in A269442.

Sequence in context: A067502 A318752 A123693 * A111727 A277630 A231018

Adjacent sequences:  A269524 A269525 A269526 * A269528 A269529 A269530

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Feb 29 2016

STATUS

approved

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Last modified May 19 20:41 EDT 2019. Contains 323410 sequences. (Running on oeis4.)