

A183101


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


3



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
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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


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: A059098 A082050 A183098 * A285309 A250096 A162687
Adjacent sequences: A183098 A183099 A183100 * A183102 A183103 A183104


KEYWORD

nonn


AUTHOR

Jaroslav Krizek, Dec 25 2010


STATUS

approved



