A155457 a(n) = exp(Lambda(n)), where Lambda(n) is the von Mangoldt function for odd (!) primes.

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

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-François Alcover, Jan 27 2014 *)

Crossrefs

Cf. A014963.

Sequence in context: A090585 A309391 A147661 * A274658 A274660 A327531

Adjacent sequences: A155454 A155455 A155456 * A155458 A155459 A155460

Keyword

nonn

Author

Peter Luschny, Jan 22 2009, Jan 25 2009

Status

approved