A034173 - OEIS

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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 (list; graph; refs; listen; history; text; internal format)

	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`
	STATUS	`approved`

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Last modified August 29 18:55 EDT 2024. Contains 375518 sequences. (Running on oeis4.)