%I #35 Feb 09 2021 01:56:33

%S 8,15,17,37,41,46,51,53,55,65,75,77,102,106,110,116,130,131,138,140,

%T 147,157,158,165,166,167,178,180,183,192,197,217,222,225,233,235,251,

%U 258,285,287,302,310,315,321,325,328,333,336,340,355,368,371,377,380,393,416,418,420,430,432,441,447

%N Exceptional class of numbers k such that p(5k+4) == 0 (mod 25), where p() = A000041().

%C The unexceptional class consists of the numbers k == 4 (mod 5).

%C (p(5*a(m) + 4)/25: m >= 1) = (3007, 553946, 1999837, 61090943985, 341143252095, 2634063438811, 18381830017947, 38993374797785, 81633034103003, ...) - _Petros Hadjicostas_, Sep 23 2019

%H Watson, G. N., <a href="http://www.digizeitschriften.de/dms/resolveppn/?PID=GDZPPN002174499">Ramanujans Vermutung über Zerfällungsanzahlen</a>, J. Reine Angew. Math. (Crelle) 179 (1938), 97-128; see p. 113.

%p isA160524 := n -> 0 = modp(combinat:-numbpart(5*n + 4), 25) and 4 <> modp(n, 5):

%p select(isA160524, [$1..200]); # _Petros Hadjicostas_, Sep 23 2019

%Y Cf. A000041, A071734, A327713, A327714.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Nov 13 2009

%E More terms from _Petros Hadjicostas_, Sep 23 2019