OFFSET
1,2
COMMENTS
Numbers k such that A235137(k) == 8 (mod k).
A positive integer k is a 8-Sondow number if satisfies any of the following equivalent properties:
1) p^s divides k/p + 8 for every prime power divisor p^s of k.
2) 8/k + Sum_{prime p|k} 1/p is an integer.
3) 8 + Sum_{prime p|k} k/p == 0 (mod k).
4) Sum_{i=1..k} i^phi(k) == 8 (mod k).
Other numbers in the sequence: 17716019376, 419963172816, 67923372668477507285654170088688
LINKS
Github, Jonathan Sondow (1943 - 2020)
J. M. Grau, A. M. Oller-Marcén and D. Sadornil, On µ-Sondow Numbers, arXiv:2111.14211 [math.NT], 2021.
J. M. Grau, A. M. Oller-Marcen and J. Sondow, On the congruence 1^n + 2^n + ... + n^n = d (mod n), where d divides n, arXiv:1309.7941 [math.NT], 2013-2014.
MATHEMATICA
Sondow[mu_][n_]:=Sondow[mu][n]=Module[{fa=FactorInteger[n]}, IntegerQ[mu/n+Sum[1/fa[[i, 1]], {i, Length[fa]}]]]
Select[Range[400000], Sondow[8][#]&]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
José María Grau Ribas, Feb 04 2022
EXTENSIONS
a(8)-a(9) verified by Martin Ehrenstein, Feb 04 2022
STATUS
approved