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

1,2

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..16385

Index entries for sequences related to sums of divisors

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.

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000203, A091051, A183098, A183105.

Sequence in context: A353956 A367633 A183098 * A343300 A285309 A250096

Adjacent sequences: A183098 A183099 A183100 * A183102 A183103 A183104

Keyword

nonn

Author

Jaroslav Krizek, Dec 25 2010

Status

approved