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A277895
a(n) is the index of the column where n is located in array A277898, a(2) = 0.
4
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
2,3
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)
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)).
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 *)
PROG
(Scheme) (definec (A277895 n) (cond ((<= n 2) 0) ((= 1 (A010051 n)) 1) (else (+ 1 (A277895 (A277894 n))))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 08 2016
STATUS
approved