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A117825 Distance from n-th highly composite number (cf. A002182) to nearest prime. 4
1, 0, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 11, 13, 1, 11, 1, 17, 1, 1, 13, 13, 1, 1, 17, 1, 17, 1, 1, 17, 17, 17, 1, 1, 19, 37, 37, 1, 17, 23, 1, 29, 1, 1, 19, 1, 19, 23, 1, 19, 31, 1, 19, 1, 1, 1, 1, 23, 1, 29, 23, 23, 1, 23, 71, 37, 1, 1, 31, 1, 23, 53, 1, 31 (list; graph; refs; listen; history; internal format)
OFFSET

1,10

COMMENTS

a) Conjecture: entries > 1 will always be prime. The entry will be larger than the largest prime factor of the highly composite number.

b) Will 1 always be the most common entry?

c) While a prime may always located close to each highly composite number, is the converse false?

d) Is there always a prime between successive highly composite numbers?

LINKS

Charles Greathouse IV, Table of n, a(n) for n = 1..19999

Graeme McRae, Highly Composite Numbers

Wikipedia, Highly Composite Numbers.

Wikipedia, Divisor Function (sigma).

Wikimedia Commons,Alternate plot

EXAMPLE

a(5) = abs(12-11)=1.

CROSSREFS

Sequence in context: A074465 A081229 A109010 * A010143 A101027 A129408

Adjacent sequences:  A117822 A117823 A117824 * A117826 A117827 A117828

KEYWORD

nonn

AUTHOR

Bill McEachen, May 01 2006

EXTENSIONS

More terms from Don Reble (djr(AT)nk.ca), May 02 2006

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Last modified February 17 03:45 EST 2012. Contains 205978 sequences.