A175083 Number of numbers whose sum of perfect divisors is equal to n.

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, 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, 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

Offset: 1

Author

Jaroslav Krizek, Jan 24 2010

Keywords

• nonn

Comments

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).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A175067, A175081.

Programs

PARI

up_to = 65537;
A175067(n) = (n+if(!ispower(n),0,sumdiv(n,d,if((d>1)&&(dA175083list(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); };
v175083 = A175083list(up_to);
A175083(n) = v175083[n]; \\ Antti Karttunen, Sep 25 2018

Extensions

More terms from Antti Karttunen, Sep 25 2018