OFFSET
1,2
COMMENTS
The number must be strictly positive, but one of the squares may be zero, as we see from a(1) = 1 = 1^2 + 0^2 and a(2) = 25 = 3^2 + 4^2 = 5^0 + 0^2. - M. F. Hasler, Jul 07 2024
LINKS
Ray Chandler, Table of n, a(n) for n = 1..1458 (a(1459) exceeds 1000 digits).
FORMULA
a(n) = A000446(n), n > 1. - R. J. Mathar, Jun 15 2008
a(n) = min { k > 0 | A000161(k) = n }. - M. F. Hasler, Jul 07 2024
EXAMPLE
a(3) = 325 is decomposable in 3 ways: 15^2 + 10^2 = 17^2 + 6^2 = 18^2 + 1^2.
PROG
(PARI) A124980(n)={for(a=1, oo, A000161(a)==n && return(a))} \\ R. J. Mathar, Nov 29 2006, edited by M. F. Hasler, Jul 07 2024
(PARI)
PD(n, L=n, D=Vecrev(divisors(n)[^1])) = { if(n>1, concat(vector(#D, i, if(D[i] > L, [], D[i] < n, [concat(D[i], P) | P <- PD(n/D[i], D[i])], [[n]]))), [[]])}
apply( {A124980(n)=vecmin([prod(i=1, #a, A002144(i)^(a[i]-1)) | a<-concat([PD(n*2, n), PD(n*2-1)])])}, [1..44]) \\ M. F. Hasler, Jul 07 2024
(Python)
from sympy import divisors, isprime, prod
def PD(n, L=None): return [[]] if n==1 else [
[d]+P for d in divisors(n)[:0:-1] if d <= (L or n) for P in PD(n//d, d)]
A2144=lambda upto=999: filter(isprime, range(5, upto, 4))
def A124980(n):
return min(prod(a**(f-1) for a, f in zip(A2144(), P))
for P in PD(n*2, n)+PD(n*2-1)) # M. F. Hasler, Jul 07 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Nov 15 2006
EXTENSIONS
More terms from R. J. Mathar, Nov 29 2006
Edited and extended by Ray Chandler, Jan 07 2012
STATUS
approved