A165501 -id:A165501 - cp's OEIS frontend

A165499 First term of maximal arithmetic progression with difference n, such that each term k has tau(k) = n.

1, 3, 4, 5989, 16

Offset: 1

Hugo van der Sanden, Sep 21 2009; updated Nov 29 2016

a(6) <= 161804009483982959337354063701 if A165498(6) = 9, and at least 1e14.
a(8) = 380017309607.
a(10) <= 43920665884407841463671 if A165498(10) = 5 (found by Giovanni Resta), and at least 1e12.
a(12) <= 11673662470957217427690002629075 if A165498(12) = 10, and at least 1e10.
a(16) = 2a(8).
A165498(n) = 1 for odd n, so a(7) = 64; a(9) = 36; a(11) = 1024; a(13) = 4096; a(15) = 144; etc.

			A165498(4) = 8, and exhaustive search finds tau(5989) = tau(5993) = tau(5997) = tau(6001) = tau(6005) = tau(6009) = tau(6013) = tau(6017) = 4 is the first example of an 8-term progression, so a(4) = 5989.

Cf. A064491, A165497, A165498, A165501.

A165500 Maximum length of arithmetic progression starting at n such that each term k has tau(k) = tau(n).

Original entry on oeis.org

1, 2, 3, 2, 5, 3, 7, 4, 2, 5, 11, 3, 13, 7, 6, 2, 17, 3, 19, 5, 7, 11

Offset: 1

Hugo van der Sanden, Sep 21 2009, Oct 09 2009

Implicitly, we require the difference d of the arithmetic progression to be positive.

a(n) <= n for all n.

			For n=4, tau(n)=3 so each term of the arithmetic progression must be the square of a prime. The difference d must be odd for n+d to qualify, in which case n+2d is even and does not qualify; so a(4)=2 is an upper bound.

Cf. A165498, A165501, A088430.

Extended to n=22 (taking advantage of A088430 for n=19) by Hugo van der Sanden, Jun 02 2015

cp's OEIS Frontend

A165499 First term of maximal arithmetic progression with difference n, such that each term k has tau(k) = n.

Views

Author

Keywords

Comments

Examples

Crossrefs