A071166 a(n) = n - A006530(A000203(n)), difference between n and largest prime factor of the sum of its divisors.

-1, 1, -3, 2, 3, 5, 3, -4, 7, 8, 5, 6, 11, 12, -15, 14, 5, 14, 13, 19, 19, 20, 19, -6, 19, 22, 21, 24, 27, 29, 25, 30, 31, 32, 23, 18, 33, 32, 35, 34, 39, 32, 37, 32, 43, 44, 17, 30, 19, 48, 45, 50, 49, 52, 51, 52, 53, 54, 53, 30, 59, 50, -63, 58, 63, 50, 61, 66, 67, 68, 59, 36, 55, 44, 69, 74, 71, 74, 49, 70, 75, 76, 77, 82, 75, 82, 83

Offset

2,3

Comments

Terms are mostly positive. At cases when sigma(n) is prime the differences are negative. See A071167.

Links

Robert Israel, Table of n, a(n) for n = 2..10000

Example

n=12, divisors={1,2,3,4,6,12}, sigma(12)=28, its largest prime factor is 7, so a(12)=12-7=5.

Maple

gpf:= n -> max(numtheory:-factorset(n)):
seq(n - gpf(numtheory:-sigma(n)), n=2..100); # Robert Israel, Feb 12 2017

Mathematica

ma[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] t=Table[w-ma[DivisorSigma[1, w]], {w, 2, 128}]

Prog

(PARI) a(n)=n-factor(sigma(n))[1, 1] \\ Charles R Greathouse IV, Feb 19 2013

Crossrefs

Cf. A000203, A006530, A062700, A023194, A071167.

Sequence in context: A098229 A346388 A128151 * A140358 A130727 A155515

Adjacent sequences: A071163 A071164 A071165 * A071167 A071168 A071169

Keyword

sign

Author

Labos Elemer, May 15 2002

Status

approved