A128981 Numbers k such that k divides Sum_{j=1..k} j^j = A001923(k).

1, 4, 17, 19, 148, 1577, 3564, 4388, 5873, 6639, 8579, 62500, 376636, 792949, 996044, 1174065, 3333551, 5179004, 7516003

Offset: 1

Author

Alexander Adamchuk, Apr 29 2007

Keywords

• hard
• more
• nonn

Comments

a(20) > 10^7. - Hiroaki Yamanouchi, Aug 25 2015

Crossrefs

Cf. A062970, A001923.

Programs

Maple

a:=0:
for n from 1 to 2000 do
    a:=a+n^n:
    if a mod n=0 then
        print(n);
    fi;
od: # Revised program from R. J. Mathar, Jun 18 2015

Mathematica

f=0; Do[ f=f+k^k; If[ IntegerQ[f/k], Print[k] ], {k,1,6639} ]

PARI

for(n=1,10^4, s=sum(i=1,n,Mod(i,n)^i); if(!Mod(s,n), print1(n,", "))) \\ Derek Orr, Jun 18 2015

Python

from itertools import accumulate, count, islice
def A128981_gen(): # generator of terms
    yield 1
    for i, j in enumerate(accumulate(k**k for k in count(1)),start=2):
        if j % i == 0:
            yield i
A128981_list = list(islice(A128981_gen(),10)) # Chai Wah Wu, Jun 18 2022

Extensions

a(11) and a(12) from Jon E. Schoenfield, May 09 2007

a(13) = 376636 from Alexander Adamchuk, May 03 2010

a(14)-a(16) from Lars Blomberg, May 10 2011

a(17) from Giovanni Resta, Jul 13 2015

a(18)-a(19) from Hiroaki Yamanouchi, Aug 25 2015