A181485 Indices of records in A171919 = number of solutions to n=x*y*z, x+y=z+1.

1, 4, 112, 144, 23400, 28224, 247104, 604800, 26812800, 2677752000, 6805814400, 165145780800, 1248124550400, 17996854730400, 388778796252000

Offset: 1

Author

R. J. Mathar and M. F. Hasler, Oct 23 2010

Keywords

• hard
• more
• nonn

Comments

The sequence lists all n such that A171919(n) > A171919(k) for all k < n.

Also the subsequence of terms of A171920 for which A171919 is larger than for all preceding values.

The actual record values are given in A181486.

a(10) > 5*10^7.

It seems highly probable that all terms of this sequence, except for a(1) = 1, are multiples of 4.

a(14) > 4*10^12. - Donovan Johnson, Jun 14 2011

a(16) > 2*10^17. - Robert Gerbicz, Apr 10 2012

Examples

			a(1) = 1 since there is no smaller value possible.
a(2) = 4 is the smallest number for which there are more than 1 = A171919(1) solutions to n = x*y*z, x + y = z + 1.
a(3) = 112 is the smallest number for which there are more than 2 = A171919(4) solutions to n = x*y*z, x + y = z + 1.
		

Programs

PARI

m=0;for(n=1,1e9,A171919(n)>m | next; m=A171919(n); print1(n", "))

Extensions

a(10)-a(13) from Donovan Johnson, Jun 14 2011

a(14)-a(15) from Robert Gerbicz, Apr 10 2012