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A182856 a(0) = 1; for n > 0, a(n) = smallest positive integer whose prime signature contains, for k = 1 to n, exactly one positive number appearing exactly k times. 1
1, 2, 60, 1801800, 11657093261814000, 7167827541370578634694420017740000, 291943326350524088652207164949980988754136887856059678357800000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = smallest number m such that A181819(m) = A006939(n).  a(n) belongs to A182855 iff n > 1.

Next term has 105 digits.

LINKS

Table of n, a(n) for n=0..6.

D. Alpern, Factorization using the Elliptic Curve Method

FORMULA

Partial products of A113511.

log a(n) ~ (1/3) n^3 log n. [Charles R Greathouse IV, Jan 13 2012]

EXAMPLE

The canonical prime factorization of a(3) = 1801800 is 2^3*3^2*5^2*7*11*13. The prime signature of 1801800 is therefore (3,2,2,1,1,1). Note that (3,2,2,1,1,1) contains exactly one number that appears once (3), one number that appears twice (2), and one number that appears three times (1).

CROSSREFS

Cf. A006939, A181819, A182855.

Sequence in context: A231024 A121493 A078491 * A101896 A130411 A262079

Adjacent sequences:  A182853 A182854 A182855 * A182857 A182858 A182859

KEYWORD

nonn

AUTHOR

Matthew Vandermast, Jan 05 2011

STATUS

approved

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Last modified November 18 14:15 EST 2017. Contains 294893 sequences.