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

1,4

Links

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

Formula

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

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

Crossrefs

Cf. A133951, A027423.

Sequence in context: A097116 A155380 A155445 * A155348 A155269 A155322

Adjacent sequences: A133949 A133950 A133951 * A133953 A133954 A133955

Keyword

nonn

Author

Leroy Quet, Sep 30 2007

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

Status

approved