A175070 a(n) is the sum of perfect divisors of n - n, where a perfect divisor of n is a divisor d such that d^k = n for some k >= 1.

0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 3, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10

Offset: 1

Author

Jaroslav Krizek, Jan 23 2010

Keywords

• nonn

Comments

a(1) = 0, for n >=2: a(n) = sum of perfect divisors of n less than n.

a(n) > 0 for perfect powers n = A001597(m) for m > 2.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to sums of divisors

Crossrefs

Cf. A175067.

Programs

Maple

a:= n-> add(`if`(n=d^ilog[d](n), d, 0), d=numtheory[divisors](n) minus {n}):
seq(a(n), n=1..100);  # Alois P. Heinz, Dec 12 2024

PARI

A175070(n) = if(!ispower(n),0,sumdiv(n,d,if((d>1)&&(dAntti Karttunen, Jun 12 2018

PARI

first(n) = {my(res = vector(n)); for(i = 2, sqrtint(n), for(j = 2, logint(n, i), res[i^j] += i)); res} \\ David A. Corneth, Jun 12 2018

Formula

a(n) = A175067(n) - n.