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Numbers k that divide prime(k^2) - 1.
2

%I #18 Sep 27 2024 02:12:10

%S 1,2,4,6,10,11,18,20,32,90,129,188,244,678,688,756,1081,1322,1477,

%T 19758,21351,29518,43187,49978,50342,95708,182326,248253

%N Numbers k that divide prime(k^2) - 1.

%C a(29) > 3*10^5. - _Donovan Johnson_, Nov 15 2009

%C Any further terms are > 10^6. - _Lucas A. Brown_, Sep 27 2024

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A067852.py">Python program</a>.

%e 6 divides prime(6^2)-1 = 150, so 6 is a term of the sequence.

%t Select[Range[10^4], Mod[Prime[ #^2] - 1, # ] == 0 &]

%o (PARI) isok(k) = !((prime(k^2)-1) % k); \\ _Michel Marcus_, Aug 15 2021

%Y Cf. A000040, A011757, A067851.

%K nonn,more,hard

%O 1,2

%A _Joseph L. Pe_, Feb 15 2002

%E a(20)-a(28) from _Donovan Johnson_, Nov 15 2009