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 A317748 #11 Mar 05 2025 17:16:37
%S A317748 0,0,1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,2,0,1,0,1,1,1,0,0,1,0,1,2,1,0,0,0,
%T A317748 1,0,1,1,0,0,1,1,0,0,1,0,3,1,0,1,0,1,2,0,1,0,0,1,0,1,2,1,0,0,0,1,1,0,
%U A317748 0,1,1,0,0,1,0,1,3,3,0,0,0,0,0,1,0,1,1
%N A317748 Irregular triangle where T(n,k) is the number of factorizations of n into factors > 1 with GCD d = A027750(n, k).
%e A317748 Triangle begins:
%e A317748 1: 0
%e A317748 2: 0 1
%e A317748 3: 0 1
%e A317748 4: 0 1 1
%e A317748 5: 0 1
%e A317748 6: 1 0 0 1
%e A317748 7: 0 1
%e A317748 8: 0 2 0 1
%e A317748 9: 0 1 1
%e A317748 10: 1 0 0 1
%e A317748 11: 0 1
%e A317748 12: 2 1 0 0 0 1
%e A317748 13: 0 1
%e A317748 14: 1 0 0 1
%e A317748 15: 1 0 0 1
%e A317748 16: 0 3 1 0 1
%e A317748 17: 0 1
%e A317748 18: 2 0 1 0 0 1
%e A317748 19: 0 1
%e A317748 20: 2 1 0 0 0 1
%t A317748 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A317748 goc[n_,m_]:=Length[Select[facs[n],And[And@@(Divisible[#,m]&/@#),GCD@@(#/m)==1]&]];
%t A317748 Table[goc[n,d],{n,30},{d,Divisors[n]}]
%Y A317748 Row lengths are A000005. Row sums are A001055. First column is A281116. Number of nonzero terms in each row is A317751.
%Y A317748 Cf. A007562, A007716, A014963, A027750, A045778, A050370, A162247, A289509, A303386, A303546.
%Y A317748 Cf. A317752, A317755, A317757.
%K A317748 nonn,tabf
%O A317748 1,18
%A A317748 _Gus Wiseman_, Aug 06 2018
%E A317748 Name edited by _Peter Munn_, Mar 05 2025