A234367 Numbers such that gcd(sigma(n), n) != 1 and numerator(sigma(n)/n) > n.

20, 70, 80, 104, 160, 208, 272, 320, 350, 416, 464, 490, 544, 550, 650, 770, 832, 928, 1088, 1184, 1190, 1280, 1300, 1312, 1332, 1430, 1610, 1664, 1696, 1700, 1750, 1856, 1870, 1952, 2170, 2196, 2210, 2368, 2420, 2530, 2560, 2590, 2624, 2628, 2750, 2990, 3010

Offset: 1

Author

Michel Marcus, Dec 28 2013

Keywords

• nonn
• nice

Comments

For numbers in A014567, we have A017665(n) = numerator(sigma(n)/n) = sigma(n) = A000203(n), so A017665(n) > n.

For numbers in A069059, since both terms of the fraction are divisible by their GCD, A009194(n), we will have A017665(n) < A000203(n).

Here we are interested in terms of A069059 for which we still have A017665(n) > n, despite the division by the GCD.

Numbers such that sigma(n)/n > gcd(sigma(n), n) > 1. - Charlie Neder, Sep 08 2018

Examples

			For n=20, we have A000203(20) = sigma(20) = 42, and since gcd(42, 20) != 1, then A017665(20) = numerator(42/20) = numerator(21/10) = 21 < sigma(20), but still A017665(20) > 20.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10519 (First 6892 terms from Charlie Neder).

Crossrefs

Cf. A000203, A009194, A014567, A017665, A069059.

Programs

Mathematica

gnQ[n_]:=Module[{s=DivisorSigma[1,n]},GCD[s,n]!=1&&Numerator[s/n]>n]; Select[ Range[ 3100],gnQ] (* Harvey P. Dale, Jan 03 2018 *)

PARI

isok(n) = (gcd(sigma(n), n) != 1) && (numerator(sigma(n)/n) > n);