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A182139 Inverse Moebius transform of A061142 2
1, 3, 3, 7, 3, 9, 3, 15, 7, 9, 3, 21, 3, 9, 9, 31, 3, 21, 3, 21, 9, 9, 3, 45, 7, 9, 15, 21, 3, 27, 3, 63, 9, 9, 9, 49, 3, 9, 9, 45, 3, 27, 3, 21, 21, 9, 3, 93, 7, 21, 9, 21, 3, 45, 9, 45, 9, 9, 3, 63, 3, 9, 21, 127, 9, 27, 3, 21, 9, 27, 3, 105, 3, 9, 21, 21, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is multiplicative with a(p^e) = -1 + 2^(e+1).

If s is squarefree then a(s) = A048691(s).

LINKS

Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000

FORMULA

a(n) = Sum(d|n, 2^Omega(d)) = Sum(d|n, 2^A001222(d)) = Sum(d|n, A061142(d)).

EXAMPLE

a(12) = a(2^2 * 3^1) = (-1 + 2^(2+1)) * (-1 + 2^(1+1)) = 7 * 3 = 21; or, using the divisors set {1,2,3,4,6,12}: 2^0 + 2^1 + 2^1 + 2^2 + 2^2 + 2^3 = 21.

MATHEMATICA

t[n_] := DivisorSum[n, 2^PrimeOmega[#]&]; Table[t[n], {n, 100}]

CROSSREFS

Cf. A001222, A061142, A048691.

Sequence in context: A208884 A034257 A145501 * A092693 A134661 A135434

Adjacent sequences:  A182136 A182137 A182138 * A182140 A182141 A182142

KEYWORD

nonn,mult

AUTHOR

Enrique Pérez Herrero, Apr 14 2012

STATUS

approved

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Last modified January 15 18:42 EST 2019. Contains 319155 sequences. (Running on oeis4.)