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%I #20 Jul 02 2017 10:53:33
%S 1,2,4,6,8,16,12,32,64,24,30,128,36,256,48,512,1024,60,72,96,2048,
%T 4096,192,8192,144,16384,120,210,216,384,32768,65536,180,288,768,
%U 131072,262144,240,432,1536,524288,576,1048576,3072,2097152,4194304,360,420
%N Irregular triangle read by rows: row n lists numbers in the range 1 to 2^(n-1) (inclusive) that have exactly n divisors.
%C There are A001055(n) different prime signatures with n divisors.
%C If a*b*c... is a factorization of n then the corresponding prime signature is p^(a-1)*q^(b-1)*r^(c-1)... etc.
%C The corresponding term of the n-th array is obtained by arranging a>b>c>... and p<q<r<... i.e. p = 2, q = 3 and r = 5 etc.
%C The n-th row contains A001055(n) terms. Taking the first term of each row gives A005179.
%D Amarnath Murthy, A note on the Smarandache Divisor sequences, Smarandache Notions Journal, Vol. 11, 1-2-3, Spring 2000.
%H T. D. Noe, <a href="/A077569/b077569.txt">Rows n=1..300, flattened</a>
%H Amarnath Murthy and Charles Ashbacher, <a href="http://www.gallup.unm.edu/~smarandache/MurthyBook.pdf">Generalized Partitions and Some New Ideas on Number Theory and Smarandache Sequences</a>, Hexis, Phoenix; USA 2005. See Section 1.4, 1.12.
%e The row for n = 12 contains 60,72,96 and 2048, each having 12 divisors, with prime signature p^2qr, p^3q^2, p^5q, p^11.
%e The triangle begins
%e 1;
%e 2;
%e 4;
%e 6,8;
%e 16;
%e 12,32;
%e 64;
%e 24,30,128;
%e 36,256;
%e 48,512;
%e 1024;
%e 60,72,96,2048;
%e 4096;
%e 192,8192;
%e 144,16384;
%e 120,210,216,384,32768;
%e 65536;
%e 180,288,768,131072;
%e 262144;
%e 240,432,1536,524288;
%e 576,1048576;
%e 3072,2097152;
%e 4194304;
%e ...
%Y Cf. A001055, A005179, A077570, A122819.
%K nonn,tabf
%O 1,2
%A _Amarnath Murthy_, Nov 11 2002
%E More terms from _Ray Chandler_, Aug 12 2003
%E Improved definition from _T. D. Noe_, Aug 31 2008
%E Edited by _N. J. A. Sloane_, Sep 05 2008
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