%I #14 Mar 14 2019 00:29:15
%S 0,2,3,0,5,5,7,0,0,7,11,3,13,9,8,0,17,2,19,5,10,13,23,3,0,15,0,7,29,
%T 10,31,0,14,19,12,0,37,21,16,5,41,12,43,11,5,25,47,3,0,2,20,13,53,2,
%U 16,7,22,31,59,8,61,33,7,0,18,16,67,17,26,14,71,0,73,39,3,19,18,18,79,5,0
%N Sum of unitary prime divisors (A056169, A034444) of n.
%H Harry J. Smith, <a href="/A063956/b063956.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n*m) = a(n) + a(m) - a(gcd(n^2, m)) - a(gcd(n, m^2)) for all n and m > 0 (conjecture). - _Velin Yanev_, Feb 17 2019
%e Prime factors in 420 which have exponent=1 (i.e., unitary p-divisors) are {5,7}; sum = 12, so a(420)=12. (The sum of all its p-divisors, unitary and non-unitary, is A008472(420) = 17.)
%t Table[DivisorSum[n, # &, And[PrimeQ@ #, GCD[#, n/#] == 1] &], {n, 81}] (* _Michael De Vlieger_, Feb 17 2019 *)
%o (PARI) { for (n=1, 1000, f=factor(n)~; a=0; for (i=1, length(f), if (f[2, i]==1, a+=f[1, i])); write("b063956.txt", n, " ", a) ) } \\ _Harry J. Smith_, Sep 04 2009
%Y Cf. A008472, A034444, A056169-A056172, A034387.
%K nonn
%O 1,2
%A _Labos Elemer_, Sep 04 2001
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