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%I #17 Jul 15 2023 20:31:12
%S 1,12,36,144,432,1296,1728,5184,15552,20736,46656,62208,186624,248832,
%T 559872,746496,1679616,2239488,2985984,6718464,8957952,20155392,
%U 26873856,60466176,35831808,80621568,107495424,241864704,322486272
%N For an integer n with prime factorization p_1*p_2*p_3* ... *p_m let n* = (p_1+1)*(p_2+1)*(p_3+1)* ... *(p_m+1); sequence gives n* such that n* is divisible by n, ordered by increasing value of n.
%C It is not difficult to show that these numbers have the form a(n) = 3^i*4^j with j <= i <= 2j.
%H Sean A. Irvine, <a href="/A064518/b064518.txt">Table of n, a(n) for n = 1..1000</a> (terms 1..50 from Harry J. Smith)
%o (PARI) ns(n)= { local(f,p=1); f=factor(n); for(i=1, matsize(f)[1], p*=(1 + f[i, 1])^f[i, 2]); return(p) } { n=0; for (m=1, 10^9, s=ns(m); if (s%m == 0, write("b064518.txt", n++, " ", s); if (n==50, break)) ) } \\ _Harry J. Smith_, Sep 17 2009
%Y Every term is also a term of A064476.
%K nonn
%O 1,2
%A _Vladeta Jovovic_, Oct 07 2001
%E Title clarified by _Sean A. Irvine_, Jul 15 2023