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A131559 Indices of records in A078571. 0
1, 3, 7, 8, 14, 41, 270, 277, 1595, 5899, 6320, 6668 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers n such that total number of prime factors (with multiplicity) of the average of n-th twin prime pair is a record.

The records are 1,2,3,4,5,7,9,10,12,14,15,17,19,.. and the associated twin primes recorded in A086827. - R. J. Mathar, Oct 24 2007

LINKS

Table of n, a(n) for n=1..12.

FORMULA

a(n) = {n such that A001222(A014574(n)) is a record)}. a(n) = {n such that A001222{(A001359(n+1) + A006512(n+1)}/2) is a record)}. a(n) = {n such that A001222(2*A040040(n)) is a record)}. a(n) = {n such that A001222(A054735(n+1)/2) is a record)}. a(n) = {n such that A001222(A111046(n+1)/4) is a record)}.

EXAMPLE

a(1) = 1 because A078571(1) = 2, since the avergae of twin prime pair (3,5) is 4 = 2^2 is a semiprime with two prime factors (withmultiplicity).

a(2) = 3 because A078571(3) = smallomega(12) = 3.

a(3) = 7 because A078571(7) = smallomega(60) = 4.

a(4) = 8 because A078571(8) = smallomega(72) = 5.

a(5) = 14 because A078571(14) = smallomega(192) = 7.

a(6) = 41 because A078571(41) = smallomega(1152) = smallomega(2^7 * 3^2) = 9.

CROSSREFS

Cf. A001221, A001359, A006512, A014574, A078571.

Sequence in context: A093722 A309745 A002381 * A051211 A105173 A309197

Adjacent sequences:  A131556 A131557 A131558 * A131560 A131561 A131562

KEYWORD

more,nonn

AUTHOR

Jonathan Vos Post, Oct 02 2007

EXTENSIONS

More terms from R. J. Mathar, Oct 24 2007

STATUS

approved

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Last modified February 19 13:23 EST 2020. Contains 332044 sequences. (Running on oeis4.)