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 A330990 #4 Jan 08 2020 09:45:29
%S A330990 1,2,3,4,6,15,44
%N A330990 Numbers whose inverse prime shadow (A181821) has its number of factorizations into factors > 1 (A001055) equal to a power of 2 (A000079).
%C A330990 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The inverse prime shadow of n is the least number whose prime exponents are the prime indices of n.
%F A330990 A001055(A181821(a(n))) = 2^k for some k >= 0.
%e A330990 The factorizations of A181821(n) for n = 1, 2, 3, 4, 6, 15:
%e A330990 () (2) (4) (6) (12) (72)
%e A330990 (2*2) (2*3) (2*6) (8*9)
%e A330990 (3*4) (2*36)
%e A330990 (2*2*3) (3*24)
%e A330990 (4*18)
%e A330990 (6*12)
%e A330990 (2*4*9)
%e A330990 (2*6*6)
%e A330990 (3*3*8)
%e A330990 (3*4*6)
%e A330990 (2*2*18)
%e A330990 (2*3*12)
%e A330990 (2*2*2*9)
%e A330990 (2*2*3*6)
%e A330990 (2*3*3*4)
%e A330990 (2*2*2*3*3)
%t A330990 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A330990 nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]],{#1}]&,If[n==1,{},Flatten[Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]]]];
%t A330990 Select[Range[100],IntegerQ[Log[2,Length[facs[Times@@Prime/@nrmptn[#]]]]]&]
%Y A330990 The same for prime numbers (instead of powers of 2) is A330993,
%Y A330990 Factorizations are A001055, with image A045782.
%Y A330990 Numbers whose number of factorizations is a power of 2 are A330977.
%Y A330990 The least number with exactly 2^n factorizations is A330989.
%Y A330990 Cf. A033833, A045778, A045783, A181821, A305936, A318283, A318284, A330972, A330973, A330976, A330998, A331022.
%K A330990 nonn,more
%O A330990 1,2
%A A330990 _Gus Wiseman_, Jan 07 2020