

A133952


a(n) = the number of "isolated divisors" of n!. A positive divisor, k, of n is isolated if neither (k1) nor (k+1) divides n.


2



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
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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 k1 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



