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URL: https://oeis.org/A062949

⇱ A062949 - OEIS

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A062949
Multiplicative with a(p^e) = ((e+1)*p^(e+1)-(e+2)*p^e+1)/(p-1).
11
1, 3, 5, 9, 9, 15, 13, 25, 23, 27, 21, 45, 25, 39, 45, 65, 33, 69, 37, 81, 65, 63, 45, 125, 69, 75, 95, 117, 57, 135, 61, 161, 105, 99, 117, 207, 73, 111, 125, 225, 81, 195, 85, 189, 207, 135, 93, 325, 139, 207, 165, 225, 105, 285, 189, 325, 185, 171, 117, 405
OFFSET
1,2
COMMENTS
Inverse Mobius transform of A062355.
LINKS
FORMULA
a(n) = Sum_{d|n} phi(d)*tau(d).
a(n) = Sum_{k=1..n} tau(n/gcd(n, k)).
a(n) = Sum_{d|n} d*uphi(n/d), where uphi() = A047994(). - Vladeta Jovovic, Mar 16 2004
MAPLE
A062949 := proc(n) add(numtheory[phi](d)*numtheory[tau](d), d=numtheory[divisors](n)) ; end proc: # R. J. Mathar, Feb 09 2011
MATHEMATICA
f[p_, e_] := ((e+1)*p^(e+1)-(e+2)*p^e+1)/(p-1); a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 60] (* Amiram Eldar, Jul 31 2019 *)
CROSSREFS
Sequence in context: A256537 A092996 A141264 * A166651 A081500 A338655
KEYWORD
nonn,easy,mult
AUTHOR
Vladeta Jovovic, Jul 21 2001
STATUS
approved