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A188775 Numbers k such that Sum_{j=1..k} j^j == -1 (mod k). 4
1, 2, 3, 6, 14, 42, 46, 1806, 2185, 4758, 5266, 10895, 24342, 26495, 44063, 52793, 381826, 543026, 547311, 805002 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers k such that A001923(k) == -1 (mod k).

a(21) > 10^7. - Hiroaki Yamanouchi, Aug 25 2015

Numbers k such that k divides A062970(k). - Jianing Song, Feb 03 2019

LINKS

Table of n, a(n) for n=1..20.

EXAMPLE

6 is a term because 1^1 + 2^2 + 3^3 + 4^4 + 5^5 + 6^6 = 50069 and 50069 + 1 = 6 * 8345. - Bernard Schott, Feb 03 2019

MAPLE

isA188775 := proc(n) add( modp(k &^ k, n), k=1..n) ; if modp(%, n) = n-1 then true; else false; end if; end proc:

for n from 1 do if isA188775(n) then printf("%d\n", n) ; end if; end do: # R. J. Mathar, Apr 10 2011

MATHEMATICA

Union@Table[If[Mod[Sum[PowerMod[i, i, n], {i, 1, n}], n]==n-1, Print[n]; n], {n, 1, 10000}]

PROG

(PARI)

f(n)=lift(sum(k=1, n, Mod(k, n)^k));

for(n=1, 10^6, if(f(n)==n-1, print1(n, ", "))) \\ Joerg Arndt, Apr 10 2011

(PARI) m=0; for(n=1, 1000, m=m+n^n; if((m+1)%n==0, print1(n, ", "))) \\ Jinyuan Wang, Feb 04 2019

(Python)

sum = 0

for n in range(10000):

    sum += n**n

    if sum % (n+1) == 0:

        print(n+1, end=', ')

# Alex Ratushnyak, May 13 2013

CROSSREFS

Cf. A128981 (sum == 0 (mod n)), A188776 (sum == 1 (mod n)).

Cf. A057245.

Cf. A001923, A062970.

Sequence in context: A193215 A007611 A098641 * A015892 A056569 A094468

Adjacent sequences:  A188772 A188773 A188774 * A188776 A188777 A188778

KEYWORD

nonn,hard,more

AUTHOR

José María Grau Ribas, Apr 10 2011

EXTENSIONS

a(12)-a(16) from Joerg Arndt, Apr 10 2011

a(17)-a(20) from Lars Blomberg, May 10 2011

STATUS

approved

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Last modified June 15 00:00 EDT 2021. Contains 345041 sequences. (Running on oeis4.)