1,2

In other words, a(n) = min { max S | S subset of N*, sum( 1/x, x in S) = n }.

a(7) = 1243 is conjectured but not yet proved.

Little is known about the number of different sets S that achieve a(n). Paul Hanna asks if it is always true that a solution set S for n+1 must necessarily contain a solution set for n as a subset. This is true for small n, apparently, but seems to me unlikely to hold in general. - N. J. A. Sloane (njas(AT)research.att.com), Dec 31 2005

Hugo van der Sanden, PERL code for this sequence

The set S = { 1, 2, 3, 6 } gives a sum 1/1 + 1/2 + 1/3 + 1/6 = 2; exhaustive search shows that no set with a smaller maximal element can sum to 2, therefore a(2) = 6.

a(1) = 1, S = { 1 }

a(2) = 6, S = { 1 2 3 6 }

a(3) = 24, S = { 1 2 3 4 5 6 8 9 10 15 18 20 24 }

a(4) = 65, S = { 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 22 24 26 27 28 30 33 35 36 40 42 45 48 52 54 56 60 63 65 }

a(5) = 184, using this set:

{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

30 32 33 34 35 36 38 39 40 42 44 45 48 50 51 52 54 55 56 58 60 62 63 65 66

68 69 70 72 75 76 77 78 80 81 84 85 87 88 90 91 92 93 95 96 99 102 104 105

108 110 112 114 115 116 117 126 130 133 136 138 140 143 144 145 150 152 153

154 155 156 161 162 165 168 170 171 174 175 176 180 184 }

a(6) = 469, using the set:

{ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

54 55 56 57 58 60 61 62 63 64 65 66 67 68 69 70 72 74 75 76 77 78 80 81 82

84 85 86 87 88 90 91 92 93 94 95 96 98 99 100 102 104 105 106 108 110 111

112 114 115 116 117 119 120 121 122 123 124 126 128 129 130 132 133 134 135

136 138 140 141 143 144 145 147 148 150 152 153 154 155 156 159 160 161 162

164 165 168 170 171 174 175 176 177 180 182 183 184 185 186 187 188 189 190

192 195 196 198 200 201 203 204 205 207 208 209 210 212 215 216 217 220 221

222 224 225 228 230 231 232 234 238 240 242 245 246 247 248 250 252 253 255

258 259 260 261 264 266 268 270 272 273 275 276 280 282 285 286 287 288 290

294 295 297 299 300 301 304 305 306 310 312 315 319 320 322 323 324 325 328

329 330 336 340 341 344 345 348 350 351 352 354 357 360 363 364 368 370 372

375 376 377 378 380 384 385 387 390 396 400 402 405 406 407 408 413 414 416

418 424 425 429 430 432 434 435 440 442 444 448 451 455 456 460 462 465 468

469 }

Sequence in context: A007531 A130669 A101854 this_sequence A092348 A006528 A052749

Adjacent sequences: A101874 A101875 A101876 this_sequence A101878 A101879 A101880

nonn,hard,nice

hv(AT)crypt.org (Hugo van der Sanden), Jan 29 2005

Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Dec 31 2005. The example for a(6) = 469 corrected Jan 31 2008 by Hugo van der Sanden (hv(AT)crypt.org)