A323903 - OEIS

%I #10 Feb 10 2019 23:06:32

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

%T 8,8,1,2,4,3,1,4,1,3,7,2,1,5,14,12,4,3,1,9,8,3,4,2,1,8,1,2,7,5,8,4,1,

%U 3,4,12,1,6,1,2,18,3,14,4,1,5,9,2,1,8,8,2,4,3,1,9,14,3,4,2,8,5,1,16,7,6,1,4,1,3,18

%N a(n) = A002487(A122111(n)).

%H Antti Karttunen, <a href="/A323903/b323903.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A323903/a323903.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>

%F a(n) = A002487(A122111(n)) = A002487(A322865(n)).

%F a(p) = 1 for all primes p.

%o (PARI)

%o A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487

%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};

%o A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));

%o A323903(n) = A002487(A122111(n));

%Y Cf. A002487, A122111, A322865.

%Y Cf. also A323168, A323174, A323902.

%K nonn

%O 1,4

%A _Antti Karttunen_, Feb 09 2019