A034174 a(n) is minimal such that prime factorizations of a(n)-n+1, ..., a(n) have same exponents.

1, 3, 35, 19943, 204327, 380480350, 440738966079

Offset: 1

Author

Dean Hickerson, Oct 01 1998

Keywords

• hard
• nonn
• more

Comments

The final terms of the arithmetic progressions defined in A083785. - N. J. A. Sloane, Oct 18 2007

a(8) > 10^13. - Donovan Johnson, Oct 20 2009. [See Reble link for an upper limit.]

The main entry is A034173, which should be updated whenever something relevant is added here. - M. F. Hasler, Oct 28 2012

Examples

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

Links

• Don Reble, A034173(8) exists, SeqFan list, Oct 23 2012
• Index entries for sequences related to primes in arithmetic progressions

Crossrefs

Diagonal of A083785. Cf. A034173, A083785, A083787. See A034173 for more.

Programs

PARI

A034174(n)={my(f); for(k=n, oo, f=0; for(i=0, n-1, f==(f=vecsort(factor(k-i)[, 2])) || !i || [k+=n-i-1; next(2)]); return(k))} \\ For illustrative purpose; not useful for n>=6. - M. F. Hasler, Oct 28 2012

Formula

a(n) = A034173(n) + n - 1. - Max Alekseyev, Nov 10 2009

Extensions

a(7) from Donovan Johnson, Oct 20 2009