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A308056 a(1) = 1, a(n) is the sum of the divisors d of n such that d and n are exponentially coprime. 1
1, 2, 3, 2, 5, 6, 7, 6, 3, 10, 11, 6, 13, 14, 15, 10, 17, 6, 19, 10, 21, 22, 23, 18, 5, 26, 12, 14, 29, 30, 31, 30, 33, 34, 35, 6, 37, 38, 39, 30, 41, 42, 43, 22, 15, 46, 47, 30, 7, 10, 51, 26, 53, 24, 55, 42, 57, 58, 59, 30, 61, 62, 21, 34, 65, 66, 67, 34, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequence of the number of those divisors is A072911.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

László Tóth, On certain arithmetic functions involving exponential divisors, Annales Univ. Sci. Budapest., Sect. Comp., Vol. 24 (2004), pp. 285-294, arXiv preprint, arXiv:math/0610274v2 [math.NT] (2006).

FORMULA

Multiplicative with a(p^e) = Sum_{i=1..e, gcd(i,e)=1} p^i.

MATHEMATICA

fun[p_, e_] := Sum[If[GCD[i, e]==1, p^i, 0], {i, 1, e}]; a[1] = 1; a[n_] := Times @@ (fun @@@ FactorInteger[n]); Array[a, 100]

CROSSREFS

Cf. A072911.

Sequence in context: A254503 A186646 A309108 * A293303 A110500 A161871

Adjacent sequences:  A308053 A308054 A308055 * A308057 A308058 A308059

KEYWORD

nonn,mult

AUTHOR

Amiram Eldar, May 10 2019

STATUS

approved

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Last modified September 20 08:13 EDT 2019. Contains 327214 sequences. (Running on oeis4.)