# Self Power Numbers - Unfinished business!

N. J. A. Sloane njas at research.att.com
Sat Feb 2 16:01:58 CET 2008

```On Feb 2, 2008 7:01 PM, N. J. A. Sloane <njas at research.att.com> wrote:
> The number N=325648 might be called a self-power number because:
> "3" means "a cube is visible in N"     (yes, it is "8" -- 8=2*2*2)
> "2" means "a square is visible in N"    (yes, it is "25" -- 25=5*5)
> "5" means "a power 5 is visible in N"     (yes, it is "32" = 2*2*2*2*2)
> "6" means "a power 6 is visible in N"     (yes, it is "64" = 2*2*2*2*2*2)
> "4" means "a power 4 is visible in N"     (yes, it is "256" = 4*4*4*4*)
> "8" means "a power 8 is visible in N"     (yes, it is "256" =2*2*2*2*2*2*2*2)
> ["visible" means "as a whole": "25" is NOT visible in 235]
> Can someone compute all such SPN _which don't include any 0's or 1's_ ?
> Feb 02 2008:  Would someone kindly work out the first few SPN's
> and send them to me? Better use email, the OEIS machine is down.

the unoptimized PARI code I include below gives:
32564,232564,256432,322564,325642,325643,325644,325645,325646,325648,325664,
332564,432564,532564,632564,643256,832564,

Regards,
Maximilian

isSPN(n)={ local( V=Vec(Str(n)), S=eval(Set(V)), t); S[1]<2 & return;
/* disallow 0 ot 1*/
t=eval( Set( concat( vector( #V,a,vector( a,b,concat( vecextract(
V,2^a-2^(b-1))))))));
for(i=1,#S, for(j=1,#t, floor(sqrtn(t[j]+.5,S[i]))^S[i]==t[j] &
next(2) /*OK: goto next power*/);
return /*not OK*/); n}

for(n=1,10^9, isSPN(n) |next; print1(n","))

```