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 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