

A131559


Indices of records in A078571.


0



1, 3, 7, 8, 14, 41, 270, 277, 1595, 5899, 6320, 6668
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OFFSET

1,2


COMMENTS

Numbers n such that total number of prime factors (with multiplicity) of the average of nth 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



