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

1,2

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)

Links

Table of n, a(n) for n=1..7.

Don Reble, A034173(8) exists, SeqFan list, 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

Example

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

Prog

(PARI) A034173(n)={my(f); for(k=1, 9e9, 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

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

Sequence in context: A269632 A083459 A368899 * A132519 A117969 A003820

Adjacent sequences: A034170 A034171 A034172 * A034174 A034175 A034176

Keyword

hard,nonn,more

Author

Dean Hickerson, Oct 01 1998

Extensions

a(7) from Donovan Johnson, Oct 20 2009

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

Status

approved