A336556 - OEIS

%I #8 Jul 27 2020 21:09:32

%S 1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,0,1,1,0,0,

%T 0,1,1,1,1,0,1,0,1,1,1,0,1,1,1,1,1,0,1,1,0,1,0,0,1,1,1,1,1,1,0,0,1,1,

%U 0,0,1,1,1,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,1,0,1,1,0

%N a(n) = 1 if A336456(n) = Product_{p^e|n} A336456(p^e), and 0 otherwise. Here each p^e is the maximal power of prime p that divides k, and A336456(n) = A335915(sigma(sigma(n))).

%H Antti Karttunen, <a href="/A336556/b336556.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F For all n >= 1, a(n) >= A336546(n).

%o (PARI)

%o is_fun_mult_on_n(fun,n) = { my(f=factor(n)); prod(k=1,#f~,fun(f[k,1]^f[k,2]))==fun(n); };

%o A000265(n) = (n>>valuation(n,2));

%o A335915(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265((f[k,1]^2)-1)^f[k,2]))); };

%o A336456(n) = A335915(sigma(sigma(n)));

%o A336556(n) = is_fun_mult_on_n(A336456,n);

%Y Cf. A336557 (positions of ones), A336558 (positions of zeros), A336559, A336560.

%Y Cf. A336456, A336546.

%Y a(n) differs from A122261(1+n) for the first time at n=28, where a(28) = 1, while A122261(1+28) = 0.

%K nonn

%O 1

%A _Antti Karttunen_, Jul 25 2020