A121923 = A051177 ?

[zak seidov]

A121923  = A051177?

%I A051177
%S A051177
1,2,3,124,158,342,693,1896,3853,4434,5273,8640,14850,17928,110516,
%T A051177 178984,274534
%N A051177 Perfectly partitioned numbers: n divides
the number of partitions p(n) of n.
%D A051177 Journal of Recreational Mathematics, vol.
29, #4, pg 304, problem 2464.
%D A051177 Journal of Recreational Mathematics, vol.
30(4) 294-5 1999-2000, Soln. to prob.2464, 
               "Perfect Partitions".
%e A051177 a(4) = 124 because p(124) = 2841940500 is
divisible by 124.
%Y A051177 Cf. A000041.
%Y A051177 Sequence in context: A041813 A065842
A065841 this_sequence A095841 A004865 A006286
%Y A051177 Adjacent sequences: A051174 A051175 A051176
this_sequence A051178 A051179 A051180
%K A051177 hard,nice,nonn
%O A051177 1,2
%A A051177 M.A. Muller (MAM(AT)LAND.SUN.AC.ZA)
%E A051177 Are there infinitely many perfectly
partitioned numbers? Does there exist some n 
               for which p(n) is a perfectly
partitioned number?
%E A051177 More terms from Don Reble (djr(AT)nk.ca),
Jul 26 2002

%I A121923
%S A121923
1,2,3,124,158,342,693,1896,3853,4434,5273,8640,14850,17928
%N A121923 Numbers n such that (partition number of n)
== 0 modulo n.
%C A121923 Or n divides partition number of n. Cf.
A093952 Partition number A000041(n) mod 
               n.
%e A121923 a(7) = 693 because partition number of 693
is
%e A121923 43397921522754943172592795 =
693*62623263380598763596815;
%o A121923 (PARI)
for(n=1,20000,if(numbpart(n)%n==0,print1(n,",")))  -
(Klaus Brockhaus, Sep 
               06 2006)
%Y A121923 Cf. A000041, A093952.
%K A121923 more,nonn,new
%O A121923 1,2
%A A121923 Zak Seidov (zakseidov(AT)yahoo.com), Sep 02
2006
%E A121923 a(8) to a(14) from Klaus Brockhaus
(klaus-brockhaus(AT)t-online.de), Sep 06 2006



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