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A309542
Numbers k such that A001414(k^3+1) is divisible by k.
2
1, 2, 5, 7, 20, 24, 45, 54, 286, 1942, 30771000, 71149819, 106438598, 668274063
OFFSET
1,2
COMMENTS
a(15) > 1.5*10^9. - Giovanni Resta, Aug 07 2019
EXAMPLE
5 is a member because the prime factorization of 5^3+1=126 is 2*3^2*7 and 2+3+3+7=15 is divisible by 5.
MAPLE
filter:= proc(n) local F, t;
F:= ifactors(n^3+1)[2];
add(t[1]*t[2], t=F) mod n = 0
end proc:
select(f, [$1..10000]);
MATHEMATICA
sopfr[n_] := Total[Times @@@ FactorInteger[n]];
okQ[n_] := Divisible[sopfr[n^3+1], n];
Select[Range[10^5], okQ] (* Jean-François Alcover, May 14 2023 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
J. M. Bergot and Robert Israel, Aug 06 2019
EXTENSIONS
a(11)-a(14) from Giovanni Resta, Aug 07 2019
STATUS
approved