login
A309544
Numbers k such that A001414(k^3-1) is divisible by k.
3
1, 3, 5, 6, 8, 11, 12, 14, 20, 24, 25, 38, 54, 62, 80, 90, 110, 138, 150, 164, 168, 192, 194, 272, 278, 314, 332, 348, 398, 402, 434, 500, 572, 642, 644, 720, 728, 733, 762, 798, 812, 860, 864, 878, 920, 992, 1013, 1020, 1022, 1070, 1092, 1098, 1118, 1130, 1182, 1202, 1230, 1260, 1308, 1413, 1434
OFFSET
1,2
COMMENTS
Contains k such that k-1 and k^2+k+1 are primes. Numbers in the sequence that are not of this form include 1, 5, 11, 25, 733, 1013, 1413, 6289, 16456, and 161307. Are there infinitely many of these?
LINKS
EXAMPLE
5 is a term because the prime factorization of 5^3-1 = 124 is 2^2*31 and 2+2+31=35 is divisible by 5.
MAPLE
filter:= proc(n) local F, t, y;
F:= ifactors(n^3-1)[2];
y:= add(t[1]*t[2], t=F);
y mod n = 0
end proc:
select(filter, [$1..2000]);
MATHEMATICA
sopfr[n_] := Total[Times @@@ FactorInteger[n]];
okQ[k_] := Divisible[sopfr[k^3-1], k];
Select[Range[2000], okQ] (* Jean-François Alcover, Feb 10 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Aug 06 2019
STATUS
approved