|
|
A093195
|
|
Least number which is the sum of two distinct nonzero squares in exactly n ways.
|
|
17
|
|
|
5, 65, 325, 1105, 8125, 5525, 105625, 27625, 71825, 138125, 126953125, 160225, 1221025, 3453125, 1795625, 801125, 446265625, 2082925, 41259765625, 4005625, 44890625, 30525625, 30994415283203125, 5928325, 303460625, 53955078125, 35409725, 100140625
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
An algorithm to compute the n-th term of this sequence: Write each of 2n and 2n+1 as products of their divisors in all possible ways and in decreasing order. For each product, equate each divisor in the product to (a1+1)(a2+1)...(ar+1), so that a1 >= a2 >= a3 >= ... >= ar, and solve for the ai. Evaluate A002144(1)^a1 * A002144(2)^a2 * ... * A002144(r)^ar for each set of values determined above, then the smaller of these products is the least integer to have precisely n partitions into a sum of two distinct positive squares. [Ant King, Dec 14 2009; May 26 2010]
|
|
LINKS
|
|
|
FORMULA
|
|
|
PROG
|
(PARI) b(k)=my(c=0); for(i=1, sqrtint((k-1)\2), if(issquare(k-i^2), c+=1)); c \\ A025441
for(n=1, 10, k=1; while(k, if(b(k)==n, print1(k, ", "); break); k+=1)) \\ Derek Orr, Mar 20 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
More terms from Ant King, Dec 14 2009 and Feb 07 2010
|
|
STATUS
|
approved
|
|
|
|