A359587 - OEIS

%I #12 Jan 08 2023 15:46:03

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

%T 6,4,5,5,6,2,3,6,7,3,8,5,7,2,9,4,4,3,5,8,6,3,10,5,7,4,5,5,12,1,6,6,7,

%U 2,10,6,7,4,5,5,8,5,9,6,7,2,16,3,5,6,4,7,10,3,5,8,9,5,10,7,10,2,3,9,12,4,5,4,5,3,12

%N Fully multiplicative with a(p) = A008578(1+A329697(p)).

%H Antti Karttunen, <a href="/A359587/b359587.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A359587/a359587.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%F For n >= 1: (Start)

%F a(A000265(n)) = a(2*n) = a(n).

%F A001222(a(n)) = A087436(n),

%F A056239(a(n)) = A329697(n),

%F A318995(a(n)) = A336396(n) = A329697(A336466(n)).

%F (End)

%o (PARI)

%o A008578(n) = if(1==n,1,prime(n-1));

%o A329697(n) = if(!bitand(n, n-1), 0, 1+A329697(n-(n/vecmax(factor(n)[, 1]))));

%o A359587(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 1] = A008578(1+A329697(f[i, 1]))); factorback(f); };

%Y Cf. A000265, A001222, A008578, A056239, A087436, A318995, A329697, A336396, A336466.

%K nonn,mult

%O 1,3

%A _Antti Karttunen_, Jan 08 2023