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A309544
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Numbers k such that A001414(k^3-1) is divisible by k.
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3
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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
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OFFSET
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1,2
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COMMENTS
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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?
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LINKS
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EXAMPLE
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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.
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MAPLE
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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]);
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MATHEMATICA
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sopfr[n_] := Total[Times @@@ FactorInteger[n]];
okQ[k_] := Divisible[sopfr[k^3-1], k];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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