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A195332 Numbers such that the sum of the cube of the odd divisors is prime.

%I A195332 #12 Apr 17 2016 09:07:40
%S A195332 9,18,36,72,121,144,242,288,484,576,968,1152,1936,2304,3872,4608,7744,
%T A195332 9216,15488,18432,30976,36481,36864,61952,72361,72962,73728,123904,
%U A195332 144722,145924,146689,147456,247808,259081,289444,291848,293378,294912
%N A195332 Numbers such that the sum of the cube of the odd divisors is prime.
%C A195332 a(n) is of the form m^2 or 2*m^2.
%C A195332 See the comments in A195268 (numbers such that the sum of the odd divisors is prime).
%C A195332 It is interesting to observe that the intersection of this sequence with A195268 gives {9, 18, 36, 72, 144, 288, 576, 1152, 2304, 4608, 9216, 18432, 36864, 73728, 146689, 147456, 293378, 294912,...} and contains the sequence A005010(n) (numbers of the form 9*2^n), but is not equal to this sequence. For example, up to n = 400000, the numbers 146689 and 293378 are not divisible by 9.
%H A195332 Harvey P. Dale, <a href="/A195332/b195332.txt">Table of n, a(n) for n = 1..1000</a>
%e A195332 The divisors of 18 are  { 1, 2, 3, 6, 9, 18}, and the sum of the cube of the odd divisors 1^3 + 3^3 + 9^3 =757 is prime. Hence 18 is in the sequence.
%p A195332 with(numtheory):for n from 1 to 400000 do:x:=divisors(n):n1:=nops(x):s:=0:for m from 1 to n1 do:if irem(x[m],2)=1 then s:=s+x[m]^3:fi:od:if type(s,prime)=true  then printf(`%d, `,n): else fi:od:
%t A195332   Module[{c=Range[800]^2,m},m=Sort[Join[c,2c]];Select[m,PrimeQ[Total[ Select[ Divisors[#],OddQ]^3]]&]](* _Harvey P. Dale_, Jul 31 2012 *)
%Y A195332 Cf. A005010, A066100 (sqrt of odd numbers here), A195268.
%K A195332 nonn
%O A195332 1,1
%A A195332 _Michel Lagneau_, Sep 15 2011