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A038111 (Denominator of) frequency of integers with smallest divisor prime(n). 10
2, 6, 15, 105, 385, 1001, 17017, 323323, 7436429, 19605131, 86822723, 3212440751, 131710070791, 5663533044013, 266186053068611, 613385252723321, 2783825377744303, 5855632691117327, 392327390304860909 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Denominator of (prod_{k=1..n-1} (1 - 1/prime(k)))/prime(n). - Vladimir Shevelev, Jan 09 2015

LINKS

Robert Israel, Table of n, a(n) for n = 1..277

Fred Kline and Gerry Myerson, Identity for frequency of integers with smallest prime(n) divisor, Math Stack Exchange question

V. Shevelev, Generalized Newman phenomena and digit conjectures on primes, Internat. J. of Mathematics and Math. Sciences, 2008 (2008), Article ID 908045, 1-12 (pp. 10-11, formula (5.8))

FORMULA

a(n) = denominator of phi(e^(psi(p_n-1)))/e^(psi(p_n)), where psi(.) is the second Chebyshev function and phi(.) is Euler's totient function. - Fred Daniel Kline, Jul 17 2014

a(n) = prime(n)*A060753(n). - Vladimir Shevelev, Jan 10 2015

MAPLE

N:= 100: # for the first N terms

Q:= 1: p:= 1:

for n from 1 to N do

  p:= nextprime(p);

  A[n]:= denom(Q/p);

  Q:= Q * (1 - 1/p);

end:

seq(A[n], n=1..N); # Robert Israel, Jul 14 2014

MATHEMATICA

Denominator@Table[ Product[ 1-1/Prime[ k ], {k, n-1} ]/Prime[ n ], {n, 1, 64} ]

(* Wouter Meeussen *)

Denominator@

Table[EulerPhi[Exp[Sum[MangoldtLambda[m], {m, 1, Prime[n] - 1}]]]/

Exp[Sum[MangoldtLambda[m], {m, 1, Prime[n]}]], {n, 1, 21}]

(* Fred Daniel Kline, Jul 14 2014 *)

CROSSREFS

Cf. A038110, A060753.

Sequence in context: A007709 A190339 A078328 * A261726 A181993 A123475

Adjacent sequences:  A038108 A038109 A038110 * A038112 A038113 A038114

KEYWORD

nonn,frac

AUTHOR

Wouter Meeussen

STATUS

approved

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Last modified September 21 15:29 EDT 2017. Contains 292307 sequences.