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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. 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 23 21:56 EST 2022. Contains 350515 sequences. (Running on oeis4.)