A045983 Numbers k such that n or more consecutive integers starting at k have the same number of distinct prime divisors.

1, 2, 2, 2, 54, 91, 141, 141, 44360, 48919, 218972, 526095, 526095, 526095, 17233173, 127890362, 29138958036, 118968284928, 118968284928, 585927201062, 585927201062, 585927201062, 585927201062, 313978488186061, 453918847597184, 453918847597184, 455626105596320

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

a(n) = smallest number k such that the n numbers from k through n+k-1 have the same number of prime divisors.

a(24) > 10^12. - Donovan Johnson, Mar 29 2013

a(28) > 2 * 10^15. - Toshitaka Suzuki, Jun 22 2025

Examples

			a(5) = 54 as 54, 55, 56, 57, 58 all have 2 prime divisors.
		

Crossrefs

Cf. A006049, A075028, A075031.

Programs

PARI

v=vector(16); n=0; c1=0; for(k=1, 127890377, c2=omega(k); if(c1==c2, n++; if(v[n]==0, v[n]=k-n+1; print(n " " v[n])), n=1; c1=c2)) /* Donovan Johnson, Mar 29 2013 */

Extensions

a(18)-a(23) from Donovan Johnson, Mar 29 2013

a(24)-a(27) from Toshitaka Suzuki, Jun 22 2025