1,3

Local minima of Euler's phi function - Walter Nissen

Number of potential primes in a modulus primorial(n+1) sieve - Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 20 2000

Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 21 2009: (Start)

Equals (-1)^n * (1, 1, 1, 2, 8, 48,...) dot (-1, 2, -3, 5, -7, 11,...).

a(6) = 480 = (1, 1, 1, 2, 8, 48) dot (-1, 2, -3, 5, -7, 11) = (-1, 2, -3, 10, -56, 528). (End)

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Andrew V. Sutherland, Order Computations in Generic Groups, Ph. D. Dissertation, Math. Dept., M.I.T., 2007.

T. D. Noe, Table of n, a(n) for n=1..100

Walter Nissen, Home Page (listed in lieu of email address)

Larry Deering, The Black Key Sieve, Box 275, Bellport NY 11713-0275, 1998.

F. Ellermann, Illustration for A002110, A005867, A038110, A060753

Dennis Martin, About this sequence

Andrew V. Sutherland, Order Computations in Generic Groups, Ph. D. Dissertation, Math. Dept., M.I.T., 2007.

phi(product of first n primes), where phi = A000010.

Prod_{k=1..n} prime(k)-1.

Comment from Dennis Martin (dennis.martin(AT)dptechnology.com), Jul 16 2006: "This is also the number of composite numbers that will have the indexed prime as their lowest prime factor within any interval of the primorial of that next prime factor starting after p.

"For example, for p(4) = 7 there are a(4) = 8 composite numbers that have p(4) as their lowest prime factor in the interval of p(4)# = 210 from p(4) + 1 to p(4) + p(4)# = 217, those 8 being {49, 77, 91, 119, 133, 161, 203, 217}.

"And then there are a(4) = 8 composite numbers that have p(4) = 7 as their lowest prime factor in every subsequent interval of p(4) = 210, such as {259, 287, 301, 329, 343, 371, 413, 427} from 218 to 427 and each element is offset by 210n from the first interval."

a(4): the mod 30 prime remainder set sieve representation yields the remainder set: {1, 7, 11, 13, 17, 19, 23, 29}, 8 elements.

with (numtheory):a:=n->mul(-1+ithprime(j), j=1..n):seq(a(n), n=0..18); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 24 2008]

Table[ Product[ EulerPhi[ Prime[ j ] ], {j, 1, n} ], {n, 1, 20} ]

(PARI) for(n=0, 22, print(prod(k=1, n, prime(k)-1)))

Cf. A002110.

Sequence in context: A112541 A052667 A006925 this_sequence A079802 A009741 A009745

Adjacent sequences: A005864 A005865 A005866 this_sequence A005868 A005869 A005870

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).