The On-Line Encyclopedia of Integer Sequences (OEIS)

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A093449

Least number with n distinct prime divisors arising as the product of two or more consecutive integers.
(history; published version)

#8 by N. J. A. Sloane at Thu Dec 05 19:56:47 EST 2013

AUTHOR

_Amarnath Murthy (amarnath_murthy(AT)yahoo.com), _, Apr 03 2004

Discussion

Thu Dec 05

19:56

OEIS Server: https://oeis.org/edit/global/2075

#7 by Russ Cox at Fri Mar 30 17:38:03 EDT 2012

EXTENSIONS

Edited, corrected and extended by _David Wasserman (dwasserm(AT)earthlink.net), _, Mar 21 2007

Discussion

Fri Mar 30

17:38

OEIS Server: https://oeis.org/edit/global/184

#6 by Russ Cox at Fri Mar 30 17:34:55 EDT 2012

EXTENSIONS

a(14)-a(17) from _Donovan Johnson (donovan.johnson(AT)yahoo.com), _, Sep 13 2008

Discussion

Fri Mar 30

17:34

OEIS Server: https://oeis.org/edit/global/163

#5 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

COMMENTS

2, 6, 30, 210, and 510510 are primorials (A002110). There are no more primorials in the first 300 terms.

KEYWORD

hard,nonn,new

#4 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

DATA

2, 6, 30, 210, 2730, 39270, 510510, 23393370, 363993630, 64790866140, 530514844860, 126408523110870, 3425113062060690, 660393717163700520, 26657280574571657010, 3448055881024876471350, 308480161111936386482910

KEYWORD

hard,more,nonn,new

EXTENSIONS

a(14)-a(17) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Sep 13 2008

#3 by N. J. A. Sloane at Fri May 11 03:00:00 EDT 2007

NAME

Least number with n distinct prime divisors arising as the product of successive two or more consecutive integers.

DATA

2, 6, 60, 30, 210, 55440, 2402402730, 39270, 510510, 23393370, 363993630, 64790866140, 530514844860, 126408523110870, 3425113062060690

COMMENTS

2, 6, and 30, 210 , and 510510 are primorials (A002110), 210 = 2*3*5*7. Conjecture: There are no other primorial more primorials in the first 300 terms. (2) a(n) == 0 (mod primorial(n)).

Upper bounds for a(14)-a(18): 660393717163700520, 28386773771493397260, 3448055881024876471350, 308480161111936386482910, 32521466098360753728404190.

EXAMPLE

a(137) =240240 510510 =10*11*12*13 714*14 715 has prime divisors 2, 3, 5, 7, 11, 13 and 17.

CROSSREFS

Cf. A002110, A045619, A093450.

KEYWORD

hard,more,nonn,new

EXTENSIONS

Edited, corrected and extended by David Wasserman (dwasserm(AT)earthlink.net), Mar 21 2007

#2 by N. J. A. Sloane at Sun Feb 20 03:00:00 EST 2005

COMMENTS

2,6, and 210 are primorials (A002110), 210 = 2*3*5*7. Conjecture: There are no other primorial terms. (2) a(n) == 0 (mod primorial(n)).

KEYWORD

more,nonn,new

#1 by N. J. A. Sloane at Sat Jun 12 03:00:00 EDT 2004

NAME

Least number with n prime divisors arising as the product of successive integers.

DATA

2, 6, 60, 210, 55440, 240240

OFFSET

1,1

COMMENTS

2,6,and 210 are primorials (A002110), 210 = 2*3*5*7. Conjecture: There are no other primorial terms. (2) a(n) == 0 (mod primorial(n)).

EXAMPLE

a(13) =240240=10*11*12*13*14 has prime divisors 2,3,5,7,11,13.

CROSSREFS

Cf. A093450.

KEYWORD

more,nonn

AUTHOR

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 03 2004

STATUS

approved