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 A053813 Numbers which are an integral multiple of the sum of their proper divisors: prime and perfect numbers. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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 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: A003174 A238463 A166070 * A116974 A031402 A019438 Adjacent sequences:  A053810 A053811 A053812 * A053814 A053815 A053816 KEYWORD nonn AUTHOR Henry Bottomley, Mar 28 2000 STATUS approved

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Last modified April 7 13:36 EDT 2020. Contains 333305 sequences. (Running on oeis4.)