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

Author

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

Keywords

• hard
• nonn
• more

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A064491, A165497, A165498, A165501.