cp's OEIS Frontend

A277892 a(n) = A001222(A048675(n)).

%I A277892 #38 Jan 11 2022 10:48:25
%S A277892 0,1,1,2,1,3,1,2,1,4,2,5,2,2,2,6,1,7,2,2,1,8,1,3,2,2,2,9,1,10,1,3,2,3,
%T A277892 2,11,2,2,1,12,1,13,3,3,1,14,2,4,2,3,2,15,1,3,1,3,4,16,3,17,3,3,2,4,1,
%U A277892 18,3,3,1,19,1,20,2,2,3,4,2,21,3,3,2,22,3,3,2,2,1,23,2,4,3,5,3,4,1,24,1,3,2,25,1,26,2,2
%N A277892 a(n) = A001222(A048675(n)).
%C A277892 For n >= 3, a(n) = index of the row where n is located in array A277898.
%H A277892 Antti Karttunen (terms 2..3465) and Hans Havermann, <a href="/A277892/b277892.txt">Table of n, a(n) for n = 2..10000</a>
%F A277892 a(A019565(n)) = a(A260443(n)) = A001222(n).
%F A277892 For all n >= 2, a(A065091(n)) = n.
%t A277892 A048675[n_] := If[n == 1, 0, Total[#[[2]]*2^(PrimePi[#[[1]]] - 1)& /@ FactorInteger[n]]];
%t A277892 a[n_] := PrimeOmega[A048675[n]];
%t A277892 Table[a[n], {n, 2, 105}] (* _Jean-François Alcover_, Jan 11 2022 *)
%o A277892 (Scheme) (define (A277892 n) (if (= 1 n) 0 (A001222 (A048675 n))))
%o A277892 (PARI)
%o A277892 A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2;
%o A277892 A277892(n) = if(1==n,0,bigomega(A048675(n)));
%o A277892 for(n=1, 3465, write("b277892.txt", n, " ", A277892(n)));
%o A277892 (Python)
%o A277892 from sympy import factorint, primepi, primefactors
%o A277892 def a001222(n): return 0 if n==1 else a001222(n//primefactors(n)[0]) + 1
%o A277892 def a048675(n):
%o A277892     if n==1: return 0
%o A277892     f=factorint(n)
%o A277892     return sum(f[i]*2**(primepi(i) - 1) for i in f)
%o A277892 def a(n): return a001222(a048675(n))
%o A277892 print([a(n) for n in range(2, 101)]) # _Indranil Ghosh_, Jun 19 2017
%Y A277892 Left inverse of A065091.
%Y A277892 Cf. A001222, A048675.
%Y A277892 Cf. A277319 (positions of ones).
%Y A277892 Cf. A000040 (positions of records), A277900.
%Y A277892 Cf. A277895 (ordinal transform from a(3) onward).
%Y A277892 Cf. A277893, A277894, A277898.
%K A277892 nonn
%O A277892 2,4
%A A277892 _Antti Karttunen_, Nov 08 2016