This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A095904 #40 Mar 15 2015 01:23:38
%S A095904 2,3,4,5,9,6,7,25,10,8,11,49,14,27,12,13,121,15,125,18,16,17,169,21,
%T A095904 343,20,81,24,19,289,22,1331,28,625,40,30,23,361,26,2197,44,2401,54,
%U A095904 42,32,29,529,33,4913,45,14641,56,66,243,36,31,841,34,6859,50,28561,88,70
%N A095904 Triangular array of natural numbers (greater than 1) arranged by prime signature.
%C A095904 The unit, 1, has the empty prime signature { } (thus not in triangle).
%C A095904 Downwards diagonals:
%C A095904 * Rightmost diagonal: smallest numbers of a given prime signature in increasing order (A025487). This defines the order of signatures used.
%C A095904 This special ordering of prime signatures (by increasing smallest numbers of a given prime signature, A181087) is unrelated to any of the 8 variants of graded lexicographic or colexicographic orderings (based on the exponents only) since it depends on the magnitudes of the prime numbers. It is not even graded by Omega(n).
%C A095904 * Second rightmost diagonal: second smallest numbers of a given prime signature (A077560). (They are not increasing anymore.)
%C A095904 Upwards diagonals:
%C A095904 * Leftmost diagonal: primes. {1} (A000040)
%C A095904 * 2nd leftmost diagonal: squares of primes. {2} (A001248)
%C A095904 * 3rd leftmost diagonal: squarefree biprimes. {1,1} (A006881)
%C A095904 * 4th leftmost diagonal: cubes of primes. {3} (A030078)
%C A095904 * 5th leftmost diagonal: signature (Achilles numbers) {1,2} (A054753)
%C A095904 * 6th leftmost diagonal: fourth powers of primes. {4} (A030514)
%C A095904 * 7th leftmost diagonal: signature (Achilles numbers) {1,3} (A065036)
%C A095904 * 8th leftmost diagonal: squarefree triprimes. {1,1,1} (A007304)
%C A095904 The Achilles numbers are nonsquarefree while not perfect powers.
%C A095904 Prime signatures are often expressed in increasing order of exponents. The decreasing order of exponents (as on the Wiki page, see links) has the advantage of listing the exponents in the same order (with the canonical factorization convention) as the smallest number of a given prime signature.
%H A095904 OEIS Wiki, <a href="http://oeis.org/wiki/Prime_signature">Prime signature</a>.
%H A095904 OEIS Wiki, <a href="http://oeis.org/wiki/Orderings">Orderings</a>.
%e A095904 343 is in the 4th left- and 4th rightmost diagonal, because it is the 4th value with the 4th prime signature {3}.
%e A095904 First 8 rows of triangular array (Cf. table link for this sequence):
%e A095904 2
%e A095904 3 4
%e A095904 5 9 6
%e A095904 7 25 10 8
%e A095904 11 49 14 27 12
%e A095904 13 121 15 125 18 16
%e A095904 17 169 21 343 20 81 24
%e A095904 19 289 22 1331 28 625 40 30
%Y A095904 Cf. A083140, A064839, A181087.
%K A095904 nonn,tabl
%O A095904 0,1
%A A095904 _Alford Arnold_, Jul 10 2004
%E A095904 Extended by _Ray Chandler_, Jul 31 2004
%E A095904 Corrected (minor) by _Daniel Forgues_, Jan 21 2011
%E A095904 Example, comments by _Daniel Forgues_, Jan 21 2011
%E A095904 Edited by _Alois P. Heinz_, Jan 23 2011
%E A095904 Edited by _Daniel Forgues_, Jan 23 2011