A133952 a(n) = the number of "isolated divisors" of n!. A positive divisor, k, of n is isolated if neither (k-1) nor (k+1) divides n.

1, 0, 1, 4, 10, 19, 43, 77, 137, 243, 497, 749, 1520, 2518, 3952, 5294, 10628, 14564, 29199, 40855, 60605, 95786, 191700, 242580, 339732, 531896, 677048, 916946, 1834106, 2332346, 4664982, 5528982, 7863685, 12164443, 16422235, 19594843

Offset: 1

Author

Leroy Quet, Sep 30 2007

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..60 (terms 1..50 from Ray Chandler)

Crossrefs

Cf. A133951, A027423.

Cf. A000142, A132881.

Programs

Maple

A133952 := proc(n) local divs,k,i,a ; divs := sort(convert(numtheory[divisors](n!), list)) ; a := 0 ; for i from 1 to nops(divs) do k := op(i,divs) ; if not k-1 in divs and not k+1 in divs then a := a+1 ; fi ; od: RETURN(a) ; end: for n from 1 do printf("%d,",A133952(n)) ; od: # R. J. Mathar, Oct 19 2007

Formula

a(n) = A027423(n) - A133951(n) = A132881(A000142(n)).

Extensions

Corrected and extended by R. J. Mathar, Oct 19 2007

a(26)-a(35) from Ray Chandler, May 28 2008

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