A110926 Smaller of the pair of distinct numbers m and n such that sigma_2(m)=sigma_2(n), where sigma_2(n) is the sum of the squares of all divisors of n.

6, 24, 30, 40, 66, 78, 102, 114, 120, 120, 130, 136, 138, 150, 168, 174, 186, 186, 215, 222, 230, 246, 258, 264, 280, 280, 282, 318, 330, 354, 360, 366, 390, 402, 408, 408, 426, 430, 438, 440, 442, 456, 474, 498, 510, 520, 534, 552, 570, 582, 600, 606, 618

Offset

1,1

Comments

There do not appear to be any pairs (m,n) such that sigma_k(m)=sigma_k(n) for k>2.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

sigma_2(m)=sigma_2(n), m<n.

Example

sigma_2(30)=1^1+2^2+3^2+5^2+6^2+10^2+15^2+30^2=1300 and sigma_2(35)=1^2+5^2+7^2+35^2=1300.

Maple

with(numtheory); sigmap := proc(p, n) convert(map(proc(z) z^p end, divisors(n)), `+`) end; SA2:=[]: for z from 1 to 1 do for m to 1500 do M:=sigmap(2, m); for n from m+1 to 1500 do N:=sigmap(2, n); if N=M then SA2:=[op(SA2), [m, n, N]] fi od od od; SA2; select(proc(z) z[1]<=1000 end, SA2); #just to shorten it a bit

Crossrefs

Cf. A001157, A002025, A002046, A063990.

Cf. A110927, A110928, A110929.

Sequence in context: A364053 A306983 A234648 * A131906 A185210 A046131

Adjacent sequences: A110923 A110924 A110925 * A110927 A110928 A110929

Keyword

nonn

Author

Walter Kehowski, Sep 23 2005

Status

approved