[seqfan] Re: Fwd: A nice (decimal) property of 78

[David Wilson]

The n with

n = a concat b, phi(n) = phi(a) * phi(b)

seem to be fairly common, e.g:

phi(78) = phi(7)*phi(8)
phi(780) = phi(7)*phi(80)
phi(897) = phi(89)*phi(7)
phi(918) = phi(91)*phi(8)
phi(1179) = phi(11)*phi(79)

The list starts

78 780 897 918 1179 1365 1776 2574 2598 2967 3168 3762 4758 5775 5796
7800 7875 7917 8217 8970 9180 9576 11790 13650 13662 13875 13896 14391
17760 18564 18858 19812 20097 25740 25935 25974 25980 27573 28776 28779

Maximilian Hasler wrote:
> (10:05) gp > for(i=11,9999,i%10|next;eulerphi(i)==eulerphi(i\10)*eulerphi(i%10)&print1(i","))
> 78,897,918,2598,4758,7917,8217,
>
> Maximilian
> PS: can one have eulerphi(i)=product(eulerphi( k-th digit of i )) for i>78 ?
> I don't think so; it seems as if there would be strict ">" for all i
> different from 78.
>
>