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A305974 a(1) = 1; for n > 1, if n = p^k for some prime p and exponent k >= 1, then a(n) = -k, otherwise a(n) = 1+A085970(n).

%I A305974 #7 Jul 02 2018 20:24:54
%S A305974 1,-1,-1,-2,-1,2,-1,-3,-2,3,-1,4,-1,5,6,-4,-1,7,-1,8,9,10,-1,11,-2,12,
%T A305974 -3,13,-1,14,-1,-5,15,16,17,18,-1,19,20,21,-1,22,-1,23,24,25,-1,26,-2,
%U A305974 27,28,29,-1,30,31,32,33,34,-1,35,-1,36,37,-6,38,39,-1,40,41,42,-1,43,-1,44,45,46,47,48,-1,49,-4,50,-1,51,52
%N A305974 a(1) = 1; for n > 1, if n = p^k for some prime p and exponent k >= 1, then a(n) = -k, otherwise a(n) = 1+A085970(n).
%H A305974 Antti Karttunen, <a href="/A305974/b305974.txt">Table of n, a(n) for n = 1..16384</a>
%F A305974 a(1) = 1; for n > 1, if n = p^k for some prime p and exponent k >= 1, then a(n) = -k, otherwise [when n is not a prime power], a(n) = 1+A085970(n) = running count from 2 onward.
%o A305974 (PARI)
%o A305974 up_to = 65537;
%o A305974 partialsums(f,up_to) = { my(v = vector(up_to), s=0); for(i=1,up_to,s += f(i); v[i] = s); (v); }
%o A305974 v065515 = partialsums(n -> (omega(n)<=1), up_to);
%o A305974 A065515(n) = v065515[n];
%o A305974 A085970(n) = (n - A065515(n));
%o A305974 A305974(n) = if(1==n,n,my(e = isprimepower(n)); if(e,-e,1+A085970(n)));
%Y A305974 Cf. A000961, A065515, A085970, A095874, A305975 (rgs-transform).
%K A305974 sign
%O A305974 1,4
%A A305974 _Antti Karttunen_, Jul 02 2018