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

1,6

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

Prog

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

Crossrefs

Cf. A175067, A175081.

Sequence in context: A335699 A177207 A161528 * A323090 A355935 A180026

Adjacent sequences: A175080 A175081 A175082 * A175084 A175085 A175086

Keyword

nonn

Author

Jaroslav Krizek, Jan 24 2010

Extensions

More terms from Antti Karttunen, Sep 25 2018

Status

approved