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A113855 Numbers whose prime factors are raised to the powers of each other.

%I A113855 #4 Oct 01 2013 17:58:22
%S A113855 72,800,6272,30375,247808,750141,1384448,37879808,189267968,235782657,
%T A113855 1313046875,1749600000,3502727631,4437573632,338751673344,
%U A113855 451508436992,634465620819,2063731785728,7863818359375,7971951402153,188153927303168
%N A113855 Numbers whose prime factors are raised to the powers of each other.
%C A113855 More precisely, n is a term iff n = prod(p_i^(sopf(n)-p_i)), where n has at least two distinct prime factors p_i and sopf(n) = A008472(n). - _Rick L. Shepherd_, Feb 02 2006
%e A113855 72 = 8*9 = 2^3*3^2. So primes 2 and 3 are raised to the power of each other.
%e A113855 800 = 2^5*5^2 = 2 to the power 5 times 5 to the power 2.
%o A113855 (PARI) allpwrfact(n) = { local(x, a, b); a = vector(50); a[1] = 2^3*3^2; a[2] = 2^5*5^2; a[3] = 2^7*7^2; a[4] = 2^11*11^2; a[5] = 2^13*13^2; a[6] = 2^17*17^2; a[7] = 2^19*19^2; a[8] = 2^23*23^2; a[9] = 2^29*29^2; a[10]= 2^31*31^2; a[11]= 2^37*37^2; a[12]= 2^41*41^2; a[13]= 3^5*5^3; a[14]= 3^7*7^3; a[15]= 3^11*11^3; a[16]= 3^13*13^3; a[17]= 3^17*17^3; a[18]= 3^19*19^3; a[19]= 3^23*23^3; a[20]= 3^29*29^3; a[21]= 3^31*31^3; a[22]= 3^37*37^3; a[23]= 2^3*2^5*3^2*3^5*5^2*5^3; a[24]= 2^3*2^7*3^2*3^7*7^2*7^3; a[25]= 2^5*2^7*5^2*5^7*7^2*7^5; a[26]= 2^5*2^11*5^2*5^11*11^2*11^5; a[27]= 3^5*3^7*5^3*5^7*7^3*7^5; a[28]=5^7*7^5; a[29]=5^11*11^5; b= vecsort(a); for(x=1, 42, if(b[x]<>0, print1(b[x]", "))) } (Shepherd)
%Y A113855 Cf. A082949 (numbers of the form p^q * q^p, p, q distinct primes), A008472 (sum of distinct prime factors of n).
%K A113855 nonn
%O A113855 1,1
%A A113855 _Cino Hilliard_, Jan 25 2006
%E A113855 Corrected by _Rick L. Shepherd_, Feb 02 2006