A318470 - OEIS

%I #8 Aug 30 2018 22:42:20

%S 1,2,2,3,2,4,2,6,3,4,2,6,2,4,4,5,2,6,2,6,4,4,2,12,3,4,6,6,2,8,2,18,4,

%T 4,4,9,2,4,4,12,2,8,2,6,6,4,2,10,3,6,4,6,2,12,4,12,4,4,2,12,2,4,6,15,

%U 4,8,2,6,4,8,2,18,2,4,6,6,4,8,2,10,5,4,2,12,4,4,4,12,2,12,4,6,4,4,4,36,2,6,6,9,2,8,2,12,8

%N Multiplicative with a(p^e) = A260443(e).

%H Antti Karttunen, <a href="/A318470/b318470.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>

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

%F For all n >= 1, A001222(a(n)) = A318306(n).

%o (PARI)

%o A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961

%o A260443(n) = if(n<2, n+1, if(n%2, A260443(n\2)*A260443(n\2+1), A003961(A260443(n\2))));

%o A318470(n) = factorback(apply(e -> A260443(e),factor(n)[,2]));

%Y Cf. A260443, A318306, A318307.

%Y Differs from A293442 for the first time at n=32, where a(32) = 18, while A293442(32) = 10.

%Y Cf. also A293216, A293217, A293443, A318469.

%K nonn,mult

%O 1,2

%A _Antti Karttunen_, Aug 30 2018