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

-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, 41, 28, -1, 18, -1, 97, 18, 14, 22, 53, -1, 16, 22, 70, -1, 30, -1, 48, 57, 20, -1, 116, 41, 57, 30, 58, -1, 96, 38, 104, 34, 26, -1, 72, -1, 28, 85, 257, 46, 54, -1

Offset

1,8

Comments

Places n where a(n) is prime are: 9, 10, 25, 27, 32, 36, 49, 64,...

Places n where a(n^2) is prime are: 3, 5, 6, 7, 8,...

Number of prime factors counted with multiplicity. - Harvey P. Dale, Jan 23 2019

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Example

a(8) = (number of prime factors)*8 - (sum of divisors) = 3*8 - (1+2+4+8) = 24 - 15 = 9.

Maple

A186170 := proc(n)
n*numtheory[bigomega](n)-numtheory[sigma](n) ;
end proc: # R. J. Mathar, Jun 15 2013

Mathematica

Table[PrimeOmega[n]n-DivisorSigma[1, n], {n, 70}] (* Harvey P. Dale, Jan 23 2019 *)

Prog

(PARI) a(n)=n*bigomega(n)-sigma(n) \\ Charles R Greathouse IV, Mar 17 2014

Crossrefs

Cf. A000203, A001222, A066959.

Sequence in context: A154483 A198560 A078887 * A020827 A154971 A021109

Adjacent sequences: A186167 A186168 A186169 * A186171 A186172 A186173

Keyword

sign,easy

Author

Irina Gerasimova, Jun 14 2013

Status

approved