A183101 a(n) = sum of divisors of n that are not perfect powers.

0, 2, 3, 2, 5, 11, 7, 2, 3, 17, 11, 23, 13, 23, 23, 2, 17, 29, 19, 37, 31, 35, 23, 47, 5, 41, 3, 51, 29, 71, 31, 2, 47, 53, 47, 41, 37, 59, 55, 77, 41, 95, 43, 79, 68, 71, 47, 95, 7, 67, 71, 93, 53, 83, 71, 107, 79, 89, 59, 163, 61, 95, 94, 2, 83, 143, 67, 121, 95, 143, 71, 137, 73, 113, 98, 135, 95, 167, 79, 157, 3, 125, 83, 219, 107, 131, 119, 167, 89, 224, 111, 163, 127, 143, 119, 191, 97, 121, 146, 87

Offset: 1

Author

Jaroslav Krizek, Dec 25 2010

Keywords

• nonn

Comments

Sequence is not the same as A183098(n): a(72) = 137, A183098(72) = 65.

Examples

			For n = 12, set of such divisors is {2, 3, 6, 12}; a(12) = 2+3+6+12=23.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16385
• Index entries for sequences related to sums of divisors

Crossrefs

Cf. A000203, A091051, A183098, A183105.

Programs

Maple

N:= 1000: # to get a(1) to a(N)
S:=  {seq(seq(i^k, i=1..floor(N^(1/k))), k=2..ilog2(N))}:
seq(convert(numtheory:-divisors(t) minus S,`+`), t=1..N); # Robert Israel, Oct 02 2014

Mathematica

Table[Total[DeleteCases[Divisors[n],?(GCD@@FactorInteger[#][[All,2]]>1&)]],{n,100}]-1 (* _Harvey P. Dale, May 30 2021 *)

PARI

a(n) = sumdiv(n, d, d*((d!=1) && !ispower(d))); \\ Michel Marcus, Oct 02 2014

Formula

a(n) = A000203(n) - A091051(n).

a(1) = 0, a(p) = p, a(pq) = p+q+pq, a(pq...z) = [(p+1)*(q+1)*…*(z+1)]-1, a(p^k) = p, for p, q = primes, k = natural numbers, pq...z = product of k (k > 2) distinct primes p, q, ..., z.