A053813 Numbers which are an integral multiple of the sum of their proper divisors: prime and perfect numbers.

2, 3, 5, 6, 7, 11, 13, 17, 19, 23, 28, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271

Offset: 1

Author

Henry Bottomley, Mar 28 2000

Keywords

• nonn

Comments

Note that numbers which are an integral multiple of the sum of their proper divisors excluding 1 (A048050) are the squares of primes (A001248).

Subsequence of A166070. - Jaroslav Krizek, Oct 06 2009

Crossrefs

Cf. A000040, A000396, A001065.

Cf. A048050, A001248.

Cf. A166070.

Programs

Maple

isA053813 := proc(n) add(1/j, j=numtheory:-divisors(n)): numer(%) = denom(%) + 1 end: select(isA053813, [$1..271]); # Peter Luschny, Oct 03 2018

Mathematica

Select[Range[300], PrimeQ[#] || DivisorSigma[1, #] == 2*#&] (* Jean-François Alcover, Jun 03 2019 *)