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A230593 a(n) = n * Sum_(q|n) 1 / q, where q are noncomposite numbers (A008578) dividing n. 1
1, 3, 4, 6, 6, 11, 8, 12, 12, 17, 12, 22, 14, 23, 23, 24, 18, 33, 20, 34, 31, 35, 24, 44, 30, 41, 36, 46, 30, 61, 32, 48, 47, 53, 47, 66, 38, 59, 55, 68, 42, 83, 44, 70, 69, 71, 48, 88, 56, 85, 71, 82, 54, 99, 71, 92, 79, 89, 60, 122, 62, 95, 93, 96, 83, 127 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For n > 1, a(n) = n + n * Sum_(p|n) 1 / p, where p are primes dividing n.

LINKS

Table of n, a(n) for n=1..66.

FORMULA

a(n) = A069359(n) + n.

a(n) = Sum_(d|n)  A080339(d) * A000027(n/d).

a(n) = A080339(n) * A000027(n), where operation * denotes Dirichlet convolution, i.e. convolution of type: a(n) = Sum_(d|n) b(d) * c(n/d).

For p, q = distinct primes, a(p) = p + 1, a(pq) = pq - 1.

EXAMPLE

For n = 6: a(6) = 6 * (1/1 + 1/2 + 1/3) = 11.

CROSSREFS

Cf. A080339, A000027, A008578.

Sequence in context: A206924 A185443 A275258 * A158523 A001615 A133689

Adjacent sequences:  A230590 A230591 A230592 * A230594 A230595 A230596

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Oct 25 2013

STATUS

approved

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Last modified August 21 13:36 EDT 2017. Contains 290890 sequences.