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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.
3
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, 2148, 2154, 2707, 2707, 2709, 2709
OFFSET
1,2
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
KEYWORD
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
a(51)-a(56) from Lucas A. Brown, Oct 02 2024
STATUS
approved