A034174 - OEIS

%I #34 Mar 17 2025 07:24:22

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

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

%C The final terms of the arithmetic progressions defined in A083785. - _N. J. A. Sloane_, Oct 18 2007

%C a(8) > 10^13. - _Donovan Johnson_, Oct 20 2009. [See Reble link for an upper limit.]

%C The main entry is A034173, which should be updated whenever something relevant is added here. - _M. F. Hasler_, Oct 28 2012

%H Don Reble, <a href="/A034173/a034173.txt">A034173(8) exists</a>, SeqFan list, Oct 23 2012

%H <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>

%F a(n) = A034173(n) + n - 1. - _Max Alekseyev_, Nov 10 2009

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

%o (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

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

%K hard,nonn,more

%O 1,2

%A _Dean Hickerson_, Oct 01 1998

%E a(7) from _Donovan Johnson_, Oct 20 2009