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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

%I

%S 1,0,1,4,10,19,43,77,137,243,497,749,1520,2518,3952,5294,10628,14564,

%T 29199,40855,60605,95786,191700,242580,339732,531896,677048,916946,

%U 1834106,2332346,4664982,5528982,7863685,12164443,16422235,19594843

%N 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.

%H Ray Chandler, <a href="/A133952/b133952.txt">Table of n, a(n) for n=1..50</a>

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

%p 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

%Y Cf. A133951, A027423.

%K nonn

%O 1,4

%A _Leroy Quet_, Sep 30 2007

%E Corrected and extended by _R. J. Mathar_, Oct 19 2007

%E a(26)-a(35) from _Ray Chandler_, May 28 2008

%E a(36)-a(50) from _Ray Chandler_, Jun 20 2008

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Last modified January 28 09:52 EST 2020. Contains 331319 sequences. (Running on oeis4.)