A034173 a(n) is minimal such that prime factorizations of a(n), ..., a(n)+n-1 have same exponents.

1, 2, 33, 19940, 204323, 380480345, 440738966073

Offset: 1

Author

Dean Hickerson, Oct 01 1998

Keywords

• hard
• nonn
• more

Comments

a(8) > 10^13. - Donovan Johnson, Oct 20 2009

Don Reble has shown that a(8) < 1.9*10^42, cf. link.

From David Wasserman, Jan 05 2019: (Start)

a(8) <= 108111092880293127811946663766147737122,

a(9) <= 6850672946809600696044301071559918192380244,

a(10) <= 96037988156124494415303285590850571857698741869620,

a(11) <= 9044737840075556371215937303485030235666252755947862558252154847122. (End)

Examples

			a(4) = 19940 because 19940, ..., 19943 all have the form p^2 q r.
		

Links

• Don Reble, A034173(8) exists, SeqFan list, Oct 23 2012.

Crossrefs

Cf. A034174.

Cf. A006558, A083790.

Cf. A052213, A052214, A175590, A218448. This sequence is the first column of A083785 and first row of A113456. The latter generalizes to arithmetic progressions with step d>=1. - M. F. Hasler, Oct 28 2012

Programs

PARI

A034173(n)={my(f);for(k=1,oo,f=0;for(i=1,n, f==(f=vecsort(factor(k+n-i)[,2])) || i==1 || [k+=n-i; next(2)]);return(k))} \\ M. F. Hasler, Oct 23 2012

Formula

a(n) = A034174(n) - n + 1. - Max Alekseyev, Nov 10 2009

a(n) = A083785(n,1) = A113456(1,n); a(2) = A052213(1), a(3) = A052214(1), a(4) = A175590(1), a(5) = A218448(1), a(6) = A218448(62) = A218448(63)-1. - M. F. Hasler, Oct 28 2012

Extensions

a(7) from Donovan Johnson, Oct 20 2009

Don Reble link repaired by N. J. A. Sloane, Oct 24 2024