1,2

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 (mathar(AT)strw.leidenuniv.nl), Oct 24 2007

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)}.

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.

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

Sequence in context: A067064 A093722 A002381 this_sequence A051211 A105173 A076683

Adjacent sequences: A131556 A131557 A131558 this_sequence A131560 A131561 A131562

easy,more,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 02 2007

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 24 2007