The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A124980 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A124980

Smallest strictly positive number decomposable in n different ways as a sum of two squares.
(history; published version)

#36 by Alois P. Heinz at Tue Jul 16 12:46:59 EDT 2024

STATUS

proposed

approved

#35 by Robert C. Lyons at Tue Jul 16 12:45:36 EDT 2024

STATUS

editing

proposed

#34 by Robert C. Lyons at Tue Jul 16 12:45:30 EDT 2024

PROG

From M. F. Hasler, Jul 07 2024: (Start)

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

for P in PD(n*2, n)+PD(n*2-1)) # (End)_M. F. Hasler_, Jul 07 2024

STATUS

approved

editing

#33 by N. J. A. Sloane at Mon Jul 15 23:36:00 EDT 2024

STATUS

proposed

approved

#32 by M. F. Hasler at Mon Jul 08 00:47:38 EDT 2024

STATUS

editing

proposed

#31 by M. F. Hasler at Mon Jul 08 00:45:54 EDT 2024

PROG

(PARI) A124980(n)=if(n>1, A000446(n), 1) \\ _From _M. F. Hasler_, Jul 07 2024: (Start)

(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])

def PD(n, L=None): # return list of products that yield [[]] if n==1 else [

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)]

for P in PD(n//d, d)]

for P in PD(n*2, n)+PD(n*2-1)) # _M. F. Hasler_, Jul 07 2024(End)

STATUS

proposed

editing

Discussion

Mon Jul 08

00:47

M. F. Hasler: Done.

#30 by M. F. Hasler at Mon Jul 08 00:08:51 EDT 2024

STATUS

editing

proposed

#29 by M. F. Hasler at Mon Jul 08 00:06:01 EDT 2024

PROG

for P in PD(n*2, n)[1:]+PD(n*2-1)) # M. F. Hasler, Jul 07 2024

Discussion

Mon Jul 08

00:08

M. F. Hasler: actually, like for Python, the PARI code given in A000446 would more naturally belong here, and be used there with if(n>1,...,0). But well...

#28 by M. F. Hasler at Mon Jul 08 00:02:57 EDT 2024

PROG

A2144=lambda upto=9**9999: filter(isprime, range(1, 5, upto, 4))

for P in PD(n*2)[:1:]+PD(n*2-1)) # M. F. Hasler, Jul 07 2024

#27 by M. F. Hasler at Sun Jul 07 23:43:15 EDT 2024

PROG

from sympy import divisors, isprime, prod

for P in PD(n*2)[:1]+PD(n*2-1)) # M. F. Hasler, Jul 07 2024