login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A233045 1^m + 2^m + ... + m^m (mod m) for primary pseudoperfect numbers m. 2
1, 1, 1, 1, 5797, 272753965, 8749232767, 1045741078641946876220133713545 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

A031971(m) (mod m) for m in A054377 = 2, 6, 42, 1806, 47058, 2214502422, 52495396602, 8490421583559688410706771261086. The known values of m for which 1^m + 2^m + ... + m^m == 1 (mod m) are m = 1, 2, 6, 42, 1806.

For any m and prime p | m, use Sum_{j=1..m} j^m == -m/p (mod p) if p-1 | m or == 0 (mod p) otherwise (see Lemma 3 in Grau et al.) and the Chinese Remainder Theorem.

LINKS

Table of n, a(n) for n=1..8.

J. M. Grau, A. M. Oller-Marcen, and J. Sondow, On the congruence 1^m + 2^m + ... + m^m == n (mod m) with n|m, arXiv:1309.7941 [math.NT].

FORMULA

a(n) = 1 for n = 1, 2, 3, 4.

EXAMPLE

The 1st primary pseudoperfect number is 2, and 1^2 + 2^2 = 5 == 1 (mod 2), so a(1) = 1.

MATHEMATICA

ps={2, 6, 42, 1806, 47058, 2214502422, 52495396602, 8490421583559688410706771261086}; fa = FactorInteger; VonStaudt[n_] := Mod[n - Sum[If[IntegerQ[n/(fa[n][[i, 1]] - 1)], n/fa[n][[i, 1]], 0], {i, Length[fa[n]]}], n]; Table[VonStaudt[ps[[i]]], {i, 1, 8}]

CROSSREFS

Cf. A031971, A054377, A231409.

Sequence in context: A238553 A282335 A164649 * A031618 A206655 A270866

Adjacent sequences:  A233042 A233043 A233044 * A233046 A233047 A233048

KEYWORD

more,nonn

AUTHOR

Jonathan Sondow, Dec 10 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 26 12:54 EDT 2022. Contains 356998 sequences. (Running on oeis4.)