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%I #12 May 05 2019 03:25:52
%S 0,2,3,4,6,11,17,19,23,27,43,43,64,74,80,82,124,124,177,185,195,214,
%T 300,300,300,328,328,334,454,454,618,618,635,677,677,677,872,936,949,
%U 949,1224,1228,1579,1587,1587,1672,2124,2124,2126,2126
%N a(n) is the number of "non-isolated divisors" of n!. A positive divisor k of n is non-isolated if either k-1 or k+1 also divides n.
%F a(n) = A027423(n) - A133952(n) = A132747(A000142(n)).
%e a(6)=11 because 1,2,3,4,5,6,8,9,10,15,16 are the non-isolated divisors of 720.
%p with(numtheory): A:=proc(n) local div, NID, i: div:=divisors(factorial(n)): NID:={}: for i to tau(factorial(n)) do if member(div[i]-1, div)=true or member(div[i]+1, div)=true then NID:= `union`(NID, {div[i]}) else end if end do: NID end proc: seq(nops(A(n)),n=1..30); # _Emeric Deutsch_, Oct 12 2007
%Y Cf. A133952, A027423.
%K more,nonn
%O 1,2
%A _Leroy Quet_, Sep 30 2007
%E Corrected and extended by _Emeric Deutsch_, Oct 12 2007
%E a(31)-a(35) from _Ray Chandler_, May 28 2008
%E a(36)-a(50) from _Ray Chandler_, Jun 20 2008
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