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A330068 Numbers k such that Sum_{i=1..k} i^A000010(k) == 2 (mod k). 9
1, 3, 4, 12, 84, 3612, 94116, 4429004844, 104990793204 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Apparently includes the sequence 2*A054377.

Additional terms include 4429004844, 104990793204, and 16980843167119376821413542522172.

a(10) > 10^13. - Giovanni Resta, Feb 27 2020

LINKS

Table of n, a(n) for n=1..9.

MATHEMATICA

G[n_, k_] := G[n, k] = Mod[Sum[PowerMod[i, k, n], {i, 1, n}], n];

Select[Range[2000], G[#, EulerPhi[#]] == 2 &]

fa=FactorInteger;

se[n_, k_] := Select[Transpose[fa[n]][[1]], IntegerQ[k/(# - 1)] &];

sumlis[li_] := Sum[li[[i]], {i, 1, Length[li]}]

Table[If[Mod[-n/se[n, EulerPhi[n]] // sumlis, n] == 2, n], {n, 1, 1000000}] // Union

PROG

(PARI) isok(n) = sumdiv(n, d, eulerphi(n/d) * Mod(d, n)^eulerphi(n)) == 2; \\ Daniel Suteu, Jan 13 2020

CROSSREFS

Cf. A000010, A054377, A007850, A330069.

Sequence in context: A018930 A127689 A307077 * A127690 A092417 A071543

Adjacent sequences:  A330065 A330066 A330067 * A330069 A330070 A330071

KEYWORD

nonn,hard,more

AUTHOR

José María Grau Ribas, Nov 30 2019

EXTENSIONS

a(8)-a(9) from Giovanni Resta, Feb 27 2020

STATUS

approved

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Last modified September 29 22:33 EDT 2022. Contains 357092 sequences. (Running on oeis4.)