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

1,1

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

Links

Table of n, a(n) for n=1..60.

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 *)

Crossrefs

Cf. A000040, A000396, A001065.

Cf. A048050, A001248.

Cf. A166070.

Sequence in context: A340076 A340150 A166070 * A116974 A031402 A019438

Adjacent sequences: A053810 A053811 A053812 * A053814 A053815 A053816

Keyword

nonn

Author

Henry Bottomley, Mar 28 2000

Status

approved