A165497 a(n) starts arithmetic progression of n terms separated by tau(a(n)), each term having the same number of divisors.

1, 3, 3, 60, 60, 201, 481, 5989, 3122037, 4434429, 13576837, 183894465, 187925171, 209072257, 1498642520, 12239200420, 20220712468, 20220712468, 875023683404, 992997544772, 2721798771116, 9770941874212, 9770941874212

Offset: 1

Author

Hugo van der Sanden, Sep 21 2009

Keywords

• hard
• nonn
• more

Comments

a(15) > 10^9.

a(19) > 10^11. - Donovan Johnson, Sep 24 2009

a(24) > 10^13. - Giovanni Resta, Aug 02 2013

Examples

			tau(60) = tau(72) = tau(84) = tau(96) = tau(108) = 12. This is the first such progression of length greater than 3, so a(4) and a(5) are both 60.
		

Crossrefs

Cf. A064491, A165498, A165499.

Programs

PARI

has(n)=my(t=numdiv(n),s=1); while(numdiv(n+=t)==t, s++); s
a(n)=my(k); while(has(k++)Charles R Greathouse IV, Apr 24 2015

Extensions

a(15)-a(18) from Donovan Johnson, Sep 24 2009

a(19)-a(23) from Giovanni Resta, Aug 02 2013