A318469 - OEIS

%I #7 Aug 30 2018 22:42:27

%S 1,2,2,3,2,4,2,5,3,4,2,6,2,4,4,10,2,6,2,6,4,4,2,10,3,4,5,6,2,8,2,7,4,

%T 4,4,9,2,4,4,10,2,8,2,6,6,4,2,20,3,6,4,6,2,10,4,10,4,4,2,12,2,4,6,14,

%U 4,8,2,6,4,8,2,15,2,4,6,6,4,8,2,20,10,4,2,12,4,4,4,10,2,12,4,6,4,4,4,14,2,6,6,9,2,8,2,10,8

%N Multiplicative with a(p^e) = A019565(A003714(e)).

%H Antti Karttunen, <a href="/A318469/b318469.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

%F For all n >= 1, A001222(a(n)) = A318464(n).

%o (PARI)

%o A003714(n) = { my(s=0,w); while(n>2, w = A072649(n); s += 2^(w-1); n -= fibonacci(w+1)); (s+n); }

%o A072649(n) = { my(m); if(n<1, 0, m=0; until(fibonacci(m)>n, m++); m-2); }; \\ From A072649

%o A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565

%o A318469(n) = factorback(apply(e -> A019565(A003714(e)),factor(n)[,2]));

%Y Cf. A003714, A019565, A072649, A318464, A318465.

%Y Cf. also A293442, A293443, A300834, A318470.

%K nonn,mult

%O 1,2

%A _Antti Karttunen_, Aug 30 2018