A046421 Index of smallest repunit having exactly n prime factors (counted with multiplicity).

1, 2, 3, 13, 8, 6, 15, 12, 28, 18, 24, 32, 36, 30, 54, 42, 78, 100, 72, 176, 60, 208, 84, 132, 160, 198, 120, 204, 216, 308, 168, 280, 306, 180, 210, 264, 270, 252, 378, 336, 300

Offset: 0

Author

Patrick De Geest, Jul 15 1998

Keywords

• nonn
• more

Comments

a(40) = 300; all other subsequent terms are > 322. - Ray Chandler, Apr 23 2017

a(41) <= 684, a(42) <= 546, a(43) <= 528, a(44) <= 462, a(45) = 360, a(46) <= 576, a(47) <= 624, a(48) <= 768. - Daniel Suteu, Jan 21 2023

Examples

			For n = 5: R_6 = 111111 = 3*7*11*13*37 is the smallest repunit with five prime factors, so a(5) = 6.
		

Links

• Patrick De Geest, Repunits prime factors
• Eric Weisstein's World of Mathematics, Repunit

Crossrefs

Cf. A000042, A001222, A002275, A004022, A046053.

Initial terms of A004023, A046413, A046414, A046415, A046416, A046417, A046418, A046419.

Cf. A086565 (equivalent with distinct prime factors).

Programs

PARI

a(n) = my(k=1); while(bigomega((10^k - 1)/9) !=n, k++); k; \\ Michel Marcus, Apr 23 2017

Extensions

a(1) = 2 inserted and a(19)-a(37) added by Ray Chandler, Apr 23 2017

a(38)-a(40) from Jinyuan Wang, Apr 17 2020

Name corrected by Felix Fröhlich, Jun 04 2022