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Numbers n such that partition number p(n) == 14 (mod n).
3

%I #18 Mar 14 2015 18:43:18

%S 1,2,8,1402,3579,4111,5289,6383,6467,15146,32141,41910,82849,110088,

%T 127531,185114,1320338,1467242,5739729,22507473,32494198

%N Numbers n such that partition number p(n) == 14 (mod n).

%C No other terms below 10^8. - _Max Alekseyev_, May 19 2014

%e Partition number of 8 is 22 = 1*8 + 14, hence 8 is a term.

%e Partition number of 1402 is 52435757789401123913939450130086135644 = 37400683159344596229628709079947315*1402 + 14, hence 1402 is a term.

%t Do[ If[ Mod[ PartitionsP@n - 14, n] == 0, Print@n], {n, 731000}] (* _Robert G. Wilson v_, Sep 14 2006 *)

%o (PARI) for(n=1,200000,if((numbpart(n)-14)%n==0,print1(n,","))) \\ _Klaus Brockhaus_, Sep 07 2006

%Y Cf. A000041, A051177, A093952, A128836, A203023.

%K more,nonn

%O 1,2

%A _Zak Seidov_, Sep 02 2006

%E Edited, corrected and extended (a(1) to a(3), a(11) to a(16)) by _Klaus Brockhaus_, Sep 07 2006

%E Rechecked by _Klaus Brockhaus_, Mar 17 2007

%E a(17)-a(19) from _Ryan Propper_, Mar 17 2007

%E a(20) from _Max Alekseyev_, Dec 28 2011

%E a(21) from _Max Alekseyev_, Jan 15 2013