LINKS
David A. Corneth, <a href="/A336416/b336416_1.txt">Table of n, a(n) for n = 0..9999</a>
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Revision History for A336416
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
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reviewed
approved
STATUS
proposed
reviewed
STATUS
editing
proposed
FORMULA
From _a(p) = a(p-1) for prime p. - _David A. Corneth_, Aug 19 2020: (Start)
a(n) = -Sum_{i = 2..k} tau(n!^(1/i))*(-1)^omega(i) where i is squarefree and k is the highest power of 2 dividing n! (A011371).
a(p) = a(p-1) for prime p. (End)
STATUS
proposed
editing
STATUS
editing
proposed
LINKS
David A. Corneth, <a href="/A336416/b336416_1.txt">Table of n, a(n) for n = 0..679999</a>
FORMULA
a(p) = a(p-1) for prime p. - _From _David A. Corneth_, Aug 19 2020: (Start)
a(n) = -Sum_{i = 2..k} tau(n!^(1/i))*(-1)^omega(i) where i is squarefree and k is the 2-adic valuation of n!.
a(p) = a(p-1) for prime p. (End)
PROG
a(n) = {if(n<=3, return(1)); my(v pr = vectorprimes(primepi(n\2), ), v = vector(#pr, i, val(n, pr[i])), res = 1, cv); for(i = 2, v[1], if(issquarefree(i), cv = v\i; res-=(prod(i = 1, #cv, cv[i]+1)-1)*(-1)^omega(i) ) ); res } \\ David A. Corneth, Aug 19 2020