A175083 - OEIS

%I #10 Sep 25 2018 20:50:35

%S 1,1,1,0,1,2,1,0,0,2,1,2,1,1,1,0,1,1,1,1,1,2,1,1,0,1,0,1,1,3,1,0,1,2,

%T 1,0,1,1,1,1,1,2,1,1,1,1,1,1,0,1,1,1,1,1,1,2,1,1,1,1,1,1,1,0,1,1,1,1,

%U 1,1,1,1,1,1,1,1,1,2,1,1,0,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,0,1,1,1,1,1

%N Number of numbers whose sum of perfect divisors is equal to n.

%C Perfect divisor of m is divisor d such that d^k = m for some k >= 1. See A175067 (sum of perfect divisors of n) and A175081 (values taken by the sum of perfect divisors of n (A175067) sorted into ascending order).

%H Antti Karttunen, <a href="/A175083/b175083.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o up_to = 65537;

%o A175067(n) = (n+if(!ispower(n),0,sumdiv(n,d,if((d>1)&&(d<n)&&((d^valuation(n,d))==n),d,0))));

%o A175083list(up_to) = { my(range = Map(), v = vector(up_to), x); for(n=1,up_to,x=A175067(n); mapput(range,x,1+if(!mapisdefined(range,x), 0, mapget(range,x)))); for(n=1,up_to,v[n]=if(!mapisdefined(range,n), 0, mapget(range,n))); (v); };

%o v175083 = A175083list(up_to);

%o A175083(n) = v175083[n]; \\ _Antti Karttunen_, Sep 25 2018

%Y Cf. A175067, A175081.

%K nonn

%O 1,6

%A _Jaroslav Krizek_, Jan 24 2010

%E More terms from _Antti Karttunen_, Sep 25 2018