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.

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

Links

Table of n, a(n) for n=1..56.

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. A000142, A027423, A132747, A133952.

Sequence in context: A116853 A342334 A066615 * A166081 A111124 A295681

Adjacent sequences: A133948 A133949 A133950 * A133952 A133953 A133954

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