login
a(n) = A008475(n) - A001414(n).
2

%I #11 Nov 17 2017 20:33:32

%S 0,0,0,0,0,0,0,2,3,0,0,0,0,0,0,8,0,3,0,0,0,0,0,2,15,0,18,0,0,0,0,22,0,

%T 0,0,3,0,0,0,2,0,0,0,0,3,0,0,8,35,15,0,0,0,18,0,2,0,0,0,0,0,0,3,52,0,

%U 0,0,0,0,0,0,5,0,0,15,0,0,0,0,8,69,0,0,0,0,0,0,2,0,3,0,0,0,0,0,22,0,35,3,15

%N a(n) = A008475(n) - A001414(n).

%C a(n) is not zero if n is in A046790.

%H Antti Karttunen, <a href="/A078771/b078771.txt">Table of n, a(n) for n = 1..65537</a>

%t Array[Total[Power @@@ #] - Total[Times @@@ #] &@ FactorInteger@ # &, 100] (* _Michael De Vlieger_, Nov 17 2017, after _Olivier GĂ©rard_ at A008475 and _Ray Chandler_ at A001414 *)

%o (PARI)

%o A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ This function from _M. F. Hasler_, Feb 07 2009

%o A008475(n) = { my(f=factor(n)); vecsum(vector(#f~,i,f[i,1]^f[i,2])); };

%o A078771(n) = (A008475(n) - A001414(n)); \\ _Antti Karttunen_, Nov 17 2017

%Y Cf. A001414, A008475, A046790.

%K nonn

%O 1,8

%A _Benoit Cloitre_, Jan 11 2003