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 A387114 #8 Aug 21 2025 10:03:46
%S A387114 0,1,2,1,2,1,3,1,2,1,2,1,4,1,1,1,2,1,4,1,2,1,3,1,2,1,2,1,4,1,2,1,1,1,
%T A387114 1,1,6,1,2,1,2,1,4,1,1,1,4,1,3,1,1,1,5,1,1,1,2,1,2,1,6,1,2,1,2,1,2,1,
%U A387114 1,1,6,1,4,1,1,1,1,1,4,1,2,1,2,1,1,1,2
%N A387114 Number of divisors in common to all prime indices of n.
%C A387114 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.
%C A387114 Also the number of divisors of the greatest common divisor of the prime indices of n.
%F A387114 a(1) = 0; a(n) = A000005(A289508(n)) for n > 1.
%e A387114 The prime indices of 703 are {8,12}, with divisors {{1,2,4,8},{1,2,3,4,6,12}}, with {1,2,4} in common, so a(703) = 3.
%t A387114 Table[If[n==1,0,Length[Divisors[GCD@@PrimePi/@First/@FactorInteger[n]]]],{n,100}]
%Y A387114 For initial interval instead of divisors we have A055396.
%Y A387114 Positions of 1 are A289509, complement A318978.
%Y A387114 Positions of 2 are A387119.
%Y A387114 For prime factors or indices instead of divisors we have A387135, see A010055 or A069513.
%Y A387114 A000005 counts divisors.
%Y A387114 A001414 adds up distinct prime divisors, counted by A001221.
%Y A387114 A003963 multiplies together the prime indices of n.
%Y A387114 A112798 lists prime indices, row sums A056239 or A066328, lengths A001222.
%Y A387114 A120383 lists numbers divisible by all of their prime indices.
%Y A387114 A289508 gives greatest common divisor of prime indices.
%Y A387114 Cf. A000720, A061395, A326841, A335433, A335448, A355731, A355733, A355734, A355737, A355739, A355740, A370820.
%K A387114 nonn,new
%O A387114 1,3
%A A387114 _Gus Wiseman_, Aug 19 2025