A273787 Least number k such that A001844(k) (sums of two consecutive squares) is the sum of two nonzero squares in exactly n ways.

1, 6, 21, 23, 221, 78, 7278, 153, 703, 1653, 6695846, 496, 670758346, 8346, 1471, 1081

Offset

1,2

Comments

a(18) = 1978, a(20) = 4596, a(21) = 304153, a(22) = 137903, a(24) = 2628. - Chai Wah Wu, Feb 13 2018

Links

Table of n, a(n) for n=1..16.

Example

a(2) = 6 from 6^2 + 7^2 = 2^2 + 9^2.
a(3) = 21 from 21^2 + 22^2 = 5^2 + 30^2 = 14^2 + 27^2.
a(4) = 23 form 23^2 + 24^2 = 4^2 + 33^2 = 9^2 + 32^2 = 12^2 + 31^2.

Prog

(PARI) A025426(n)=my(v=valuation(n, 2), f=factor(n>>v), t=1); for(i=1, #f~, if(f[i, 1]%4>1, if(f[i, 2]%2, return(0)), t*=f[i, 2]+1)); if(t%2, t-(-1)^v, t)/2
a(n)=my(k=1); while(A025426(2*k*(k+1)+1)!=n, k++); k \\ Charles R Greathouse IV, Jun 03 2016

Crossrefs

Cf. A001844, A006339, A016032, A025426, A273238.

Sequence in context: A102993 A276803 A143416 * A323916 A364202 A323917

Adjacent sequences: A273784 A273785 A273786 * A273788 A273789 A273790

Keyword

nonn,more

Author

Altug Alkan, May 30 2016

Extensions

a(10)-a(14) from Giovanni Resta, Jun 03 2016

a(15)-a(16) from Chai Wah Wu, Feb 13 2018

Status

approved