A277895 a(n) is the index of the column where n is located in array A277898, a(2) = 0.

0, 1, 2, 1, 3, 1, 4, 2, 5, 1, 3, 1, 4, 5, 6, 1, 6, 1, 7, 8, 7, 1, 8, 2, 9, 10, 11, 1, 9, 1, 10, 3, 12, 4, 13, 1, 14, 15, 11, 1, 12, 1, 5, 6, 13, 1, 16, 2, 17, 7, 18, 1, 14, 8, 15, 9, 3, 1, 10, 1, 11, 12, 19, 4, 16, 1, 13, 14, 17, 1, 18, 1, 20, 21, 15, 5, 22, 1, 16, 17, 23, 1, 18, 19, 24, 25, 19, 1, 26, 6, 20, 2, 21, 7, 20, 1, 21, 22, 27, 1

Offset: 2

Author

Antti Karttunen, Nov 08 2016

Keywords

• nonn

Comments

a(2) = 0 as 2 does not occur in the array A277898 proper.

From a(3) onward the ordinal transform of A277892 from its first nonzero term a(3) onward: 1, 1, 2, 1, 3, 1, 2, 1, 4, 2, 5, 2, 2, 2, 6, 1, 7, 2, ... The relation does not hold the other way, because not all columns of A277898 are monotonic, for example, 16 is located below 18 in the sixth column of that array. Already the array's second column (A277900) is nonmonotonic.

Links

• Antti Karttunen, Table of n, a(n) for n = 2..10000 (computed from the b-file provided by _Hans Havermann_ for A277892)

Crossrefs

Cf. A010051, A277892, A277894, A277898, A277900.

Programs

Mathematica

A048675[n_] := If[n == 1, 0, Total[#[[2]]*2^(PrimePi[#[[1]]] - 1) & /@ FactorInteger[n]]];
A277892[n_] := PrimeOmega[A048675[n]];
Module[{b}, b[_] = 0;
a[n_] := If[n == 2, 0, With[{t = A277892[n]}, b[t] = b[t] + 1]]];
Table[a[n], {n, 2, 101}] (* Jean-François Alcover, Jan 11 2022 *)

Scheme

(definec (A277895 n) (cond ((<= n 2) 0) ((= 1 (A010051 n)) 1) (else (+ 1 (A277895 (A277894 n))))))

Formula

a(2)=0, for n >= 3, if A010051(n) = 1 [when n is a prime], a(n) = 1, otherwise a(n) = 1 + a(A277894(n)).