cp's OEIS Frontend

A186170 Number of prime factors times n minus sum of divisors.

%I A186170 #34 Jan 23 2025 18:34:48
%S A186170 -1,-1,-1,1,-1,0,-1,9,5,2,-1,8,-1,4,6,33,-1,15,-1,18,10,8,-1,36,19,10,
%T A186170 41,28,-1,18,-1,97,18,14,22,53,-1,16,22,70,-1,30,-1,48,57,20,-1,116,
%U A186170 41,57,30,58,-1,96,38,104,34,26,-1,72,-1,28,85,257,46,54,-1
%N A186170 Number of prime factors times n minus sum of divisors.
%C A186170 Places n where a(n) is prime are: 9, 10, 25, 27, 32, 36, 49, 64,...
%C A186170 Places n where a(n^2) is prime are: 3, 5, 6, 7, 8,...
%C A186170 Number of prime factors counted with multiplicity. - _Harvey P. Dale_, Jan 23 2019
%H A186170 Antti Karttunen, <a href="/A186170/b186170.txt">Table of n, a(n) for n = 1..20000</a>
%e A186170 a(8) = (number of prime factors)*8 - (sum of divisors) = 3*8 - (1+2+4+8) = 24 - 15 = 9.
%p A186170 A186170 := proc(n)
%p A186170 n*numtheory[bigomega](n)-numtheory[sigma](n) ;
%p A186170 end proc: # _R. J. Mathar_, Jun 15 2013
%t A186170 Table[PrimeOmega[n]n-DivisorSigma[1,n],{n,70}] (* _Harvey P. Dale_, Jan 23 2019 *)
%o A186170 (PARI) a(n)=n*bigomega(n)-sigma(n) \\ _Charles R Greathouse IV_, Mar 17 2014
%Y A186170 Cf. A000203, A001222, A066959.
%K A186170 sign,easy
%O A186170 1,8
%A A186170 _Irina Gerasimova_, Jun 14 2013