A170928 Least magic constant of magic squares using Smith numbers.

822, 1195, 1636, 2472, 3720, 5856, 8737, 12202, 16335, 21333, 27612, 35185, 43968, 54013, 65464, 78281, 92422, 107932, 126404, 147816, 171556, 197041, 224506, 253587, 285314, 320620, 359151, 400064, 442886, 487920, 536844, 589129, 644797

Offset

3,1

Comments

a(n) >= (1/n)*Sum_{i=1..n^2} A006753(i).

Links

Table of n, a(n) for n=3..35.

Natalia Makarova, Construction of smallest magic squares from Smith numbers (in Russian)

The square of order 4

The square of order 5

The square of order 6

The square of order 7

The square of order 9

Example

Magic square of order 3: see the book: M. Gardner. From the Penrose tilings to securely encrypted, 1993:
   94 382 346
  526 274  22
  202 166 454
.
The magic constant S = 822
Orders 4 to 6 are from participants of scientific forum dxdy.ru
The square of order 4:
   22 346 562 265
  778 274  85  58
    4 454 382 355
  391 121 166 517
.
S = 1195
The square of order 5:
  355 576   4 319 382
  454  85 391 648  58
   27 535 346 526 202
  706 166 378 121 265
   94 274 517  22 729
.
S = 1636
The square of order 6:
  729   4 636 762  22 319
   27 663 654 526  85 517
  391 645  58 378 438 562
  382 346 454 121 634 535
  355 648  94 483 627 265
  588 166 576 202 666 274

Crossrefs

Sequence in context: A002140 A095965 A059002 * A103764 A189121 A364538

Adjacent sequences: A170925 A170926 A170927 * A170929 A170930 A170931

Keyword

nonn,base

Author

Stefano Tognon, Feb 04 2010

Extensions

a(7), a(9) added by Natalia Makarova, Apr 02 2010

Edited by Max Alekseyev, May 26 2012

Status

approved