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A133951 a(n) is the number of "non-isolated divisors" of n!. A positive divisor k of n is non-isolated if either k-1 or k+1 also divides n. 2
0, 2, 3, 4, 6, 11, 17, 19, 23, 27, 43, 43, 64, 74, 80, 82, 124, 124, 177, 185, 195, 214, 300, 300, 300, 328, 328, 334, 454, 454, 618, 618, 635, 677, 677, 677, 872, 936, 949, 949, 1224, 1228, 1579, 1587, 1587, 1672, 2124, 2124, 2126, 2126 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..50.

FORMULA

a(n) = A027423(n) - A133952(n) = A132747(A000142(n)).

EXAMPLE

a(6)=11 because 1,2,3,4,5,6,8,9,10,15,16 are the non-isolated divisors of 720.

MAPLE

with(numtheory): A:=proc(n) local div, NID, i: div:=divisors(factorial(n)): NID:={}: for i to tau(factorial(n)) do if member(div[i]-1, div)=true or member(div[i]+1, div)=true then NID:= `union`(NID, {div[i]}) else end if end do: NID end proc: seq(nops(A(n)), n=1..30); # Emeric Deutsch, Oct 12 2007

CROSSREFS

Cf. A133952, A027423.

Sequence in context: A079310 A116853 A066615 * A166081 A111124 A295681

Adjacent sequences:  A133948 A133949 A133950 * A133952 A133953 A133954

KEYWORD

more,nonn

AUTHOR

Leroy Quet, Sep 30 2007

EXTENSIONS

Corrected and extended by Emeric Deutsch, Oct 12 2007

a(31)-a(35) from Ray Chandler, May 28 2008

a(36)-a(50) from Ray Chandler, Jun 20 2008

STATUS

approved

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Last modified October 17 14:15 EDT 2019. Contains 328113 sequences. (Running on oeis4.)