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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.

A336865 Irregular triangle read by rows where T(n,k) is the number of divisors of n with distinct prime multiplicities and a total of k prime factors, counted with multiplicity.

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%I A336865 #7 Aug 10 2020 00:23:50
%S A336865 1,1,1,1,1,1,1,1,1,1,1,2,0,1,1,1,1,1,1,1,1,1,1,2,0,1,1,1,2,1,1,1,1,1,
%T A336865 2,0,1,2,0,1,1,1,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,2,0,1,2,0,1,1,1,2,1,2,
%U A336865 1,1,1,1,1,2,0,1,1,1,1,1,2,1,1,1,1,1,3,0,0
%N A336865 Irregular triangle read by rows where T(n,k) is the number of divisors of n with distinct prime multiplicities and a total of k prime factors, counted with multiplicity.
%C A336865 Row lengths are A073093(n) = A001222(n) + 1.
%e A336865 The triangle begins as follows. The n-th row is shown to the right of "n:".
%e A336865      1: (1)          16: (1,1,1,1,1)    31: (1,1)
%e A336865      2: (1,1)        17: (1,1)          32: (1,1,1,1,1,1)
%e A336865      3: (1,1)        18: (1,2,1,1)      33: (1,2,0)
%e A336865      4: (1,1,1)      19: (1,1)          34: (1,2,0)
%e A336865      5: (1,1)        20: (1,2,1,1)      35: (1,2,0)
%e A336865      6: (1,2,0)      21: (1,2,0)        36: (1,2,2,2,0)
%e A336865      7: (1,1)        22: (1,2,0)        37: (1,1)
%e A336865      8: (1,1,1,1)    23: (1,1)          38: (1,2,0)
%e A336865      9: (1,1,1)      24: (1,2,1,2,1)    39: (1,2,0)
%e A336865     10: (1,2,0)      25: (1,1,1)        40: (1,2,1,2,1)
%e A336865     11: (1,1)        26: (1,2,0)        41: (1,1)
%e A336865     12: (1,2,1,1)    27: (1,1,1,1)      42: (1,3,0,0)
%e A336865     13: (1,1)        28: (1,2,1,1)      43: (1,1)
%e A336865     14: (1,2,0)      29: (1,1)          44: (1,2,1,1)
%e A336865     15: (1,2,0)      30: (1,3,0,0)      45: (1,2,1,1)
%e A336865 Row n = 72 counts the following divisors:
%e A336865   1  2  4   8  24  72
%e A336865      3  9  12
%e A336865            18
%e A336865 Row n = 1200 counts the following divisors:
%e A336865   1  2   4   8  16   48  400  1200
%e A336865      3  25  12  24   80  600
%e A336865      5      20  40  200
%e A336865             50
%e A336865             75
%t A336865 Table[Length[Select[Divisors[n],PrimeOmega[#]==k&&UnsameQ@@Last/@FactorInteger[#]&]],{n,20},{k,0,PrimeOmega[n]}]
%Y A336865 A073093 gives row lengths.
%Y A336865 A130092 gives positions of rows ending with 0.
%Y A336865 A146291 is the version not requiring distinct prime multiplicities.
%Y A336865 A181796 gives row sums.
%Y A336865 A336499 is the restriction to factorial numbers.
%Y A336865 A001222 counts prime factors, counting multiplicity.
%Y A336865 A008302 counts divisors of superprimorials by number of prime factors.
%Y A336865 A130091 lists numbers with distinct prime multiplicities.
%Y A336865 A181796 counts divisors with distinct prime multiplicities.
%Y A336865 A327498 gives the maximum divisor of n with distinct prime multiplicities.
%Y A336865 A336423 counts chains using A130091.
%Y A336865 Cf. A000005, A001221, A098859, A118914, A124010, A336422, A336500, A336571.
%K A336865 nonn,tabf
%O A336865 1,12
%A A336865 _Gus Wiseman_, Aug 06 2020