

A186170


Number of prime factors times n minus sum of divisors.


1



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
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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

Table of n, a(n) for n=1..67.


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]nDivisorSigma[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



