A110927 Larger 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.

7, 26, 35, 47, 77, 91, 119, 133, 130, 141, 141, 157, 161, 175, 182, 203, 215, 217, 217, 259, 249, 287, 301, 286, 282, 329, 329, 371, 385, 413, 423, 427, 455, 469, 442, 471, 497, 434, 511, 517, 471, 494, 553, 581, 595, 611, 623, 598, 665, 679, 650, 707, 721

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. A110926, A110928, A110929.

Sequence in context: A098127 A283427 A131905 * A103267 A125972 A063153

Adjacent sequences: A110924 A110925 A110926 * A110928 A110929 A110930

Keyword

nonn

Author

Walter Kehowski, Sep 23 2005

Status

approved