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A155457 a(n) = exp(Lambda(n)), where Lambda(n) is the von Mangoldt function for odd (!) primes. 2
1, 1, 3, 1, 5, 1, 7, 1, 3, 1, 11, 1, 13, 1, 1, 1, 17, 1, 19, 1, 1, 1, 23, 1, 5, 1, 3, 1, 29, 1, 31, 1, 1, 1, 1, 1, 37, 1, 1, 1, 41, 1, 43, 1, 1, 1, 47, 1, 7, 1, 1, 1, 53, 1, 1, 1, 1, 1, 59, 1, 61, 1, 1, 1, 1, 1, 67, 1, 1, 1, 71, 1, 73, 1, 1, 1, 1, 1, 79, 1, 3, 1, 83, 1, 1, 1, 1, 1, 89 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n) = p if n = p^k and p odd prime, k >= 1, otherwise 1.

REFERENCES

Tom M. Apostol, Introduction to analytic number theory, Springer-Verlag, 1976.

LINKS

Table of n, a(n) for n=1..89.

Wikipedia, Von Mangoldt function

FORMULA

a(n) = 1 + Sum_{k=3..n} (k-1)*A010051(k)*(floor(k^n/n)-floor((k^n -1)/n)). - Anthony Browne, Jun 16 2016

EXAMPLE

a(8) = 1 because 8 = 2^3 is not the power of an odd prime, a(49) = 7 because 49 = 7^2.

MAPLE

a := proc(n) local lcm; lcm := n -> ilcm(seq(i, i = 1..n)); if type(n, even) then 1 else lcm(n)/lcm(n-1) fi end;

MATHEMATICA

a[n_] := If[IntegerQ[Log[2, n]], 1, Exp[MangoldtLambda[n]]]; Table[a[n], {n, 1, 89}] (* Jean-Fran├žois Alcover, Jan 27 2014 *)

CROSSREFS

Cf. A014963.

Sequence in context: A087913 A090585 A147661 * A274658 A274660 A009001

Adjacent sequences:  A155454 A155455 A155456 * A155458 A155459 A155460

KEYWORD

nonn

AUTHOR

Peter Luschny, Jan 22 2009, Jan 25 2009

STATUS

approved

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Last modified June 21 23:01 EDT 2018. Contains 305646 sequences. (Running on oeis4.)