A274071 a(n) is the least possible sum of a sequence of distinct terms consisting of exactly prime(i) multiples of prime(i) for i = 1 to n.

6, 20, 87, 304, 1398, 3582, 9218, 18270, 34873, 70451

Offset: 1

Author

Claudio Meller, Jun 09 2016

Keywords

• nonn
• more

Comments

From R. J. Mathar, Jun 23 2016: (Start)

a(5) <= 1398 with [5 7 11 22 25 33 35 49 55 77 91 99 119 121 143 154 165 187].

a(6) <= 3582 with [7 11 13 26 33 35 39 49 55 65 77 91 117 119 121 143 169 187 209 221 247 253 286 299 325 385].

a(7) <= 9372 with [7 11 13 17 34 49 51 55 65 68 77 85 91 119 121 143 153 169 187 209 221 247 253 289 299 319 323 341 377 391 403 425 481 493 527 595 663 1001].

a(8) <= 19649 with [11 13 17 19 38 57 76 77 85 91 95 119 121 133 143 169 171 187 209 221 247 253 285 289 299 319 323 341 361 377 391 403 407 437 475 481 493 527 533 551 559 589 611 629 665 697 703 731 779 799 833 901 1309].

a(9) <= 37439. a(10) <= 74605. a(11) <= 128595. a(12) <= 215047. a(13) <= 345639. a(14) <= 506980. a(15) <= 724064. (End)

a(11-20) <= (118833, 202546, 322763, 470583, 668392, 956378, 1363577, 1830468, 2461758, 3229840). - Lars Blomberg, Oct 03 2016

Examples

			a(1) = 6 from the sequence (2,4).
a(3) = 87 (3,9,5,10,15,20,25): this sequence has only two multiples of 2, only three multiples of 3 and only five multiples of 5.
		

Links

• Claudio Meller Blog, Problem 1443, April 28 2016.
• Lars Blomberg, Details of solutions (1-10) and estimates (11-20)

Extensions

a(4) from Zak Seidov, Jun 09 2016

"Distinct terms" added to definition by N. J. A. Sloane, Jun 21 2016

a(5)-a(10) from Lars Blomberg, Oct 03 2016