# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a307114 Showing 1-1 of 1 %I A307114 #13 Mar 25 2019 19:24:10 %S A307114 27720,50400,75600,85680,95760,105840,115920,120120,128520,141120, %T A307114 143640,176400,180180,184800,205920,207900,214200,218400,235620, %U A307114 239400,264600,289800,292320,299880,308880,312480,314160,351120,371280,372960,414960,425040,438480 %N A307114 Primitive 4-abundant numbers: Numbers k such that sigma(k) > 4k (A068404) all of whose proper divisors d are 4-deficient numbers (having sigma(d) < 4d). %C A307114 Analogous to A071395 with abundancy index 4 instead of 2. %D A307114 Paul Erdős and János Surányi, Topics in the Theory of Numbers, New York: Springer, 2003, p. 243. %H A307114 Amiram Eldar, Table of n, a(n) for n = 1..10000 %H A307114 Graeme L. Cohen, Primitive alpha-abundant numbers, Mathematics of Computation, Vol. 43, No. 167 (1984), pp. 263-270. %H A307114 Paul Erdős, On additive arithmetical functions and applications of probability to number theory, Proceedings of the International Congress of Mathematicians, 1954, Amsterdam, Vol. 3 (1956), pp. 13-19. %H A307114 Paul Erdős, Remarks on number theory. I: On primitive alpha-abundant numbers, Acta Arithmetica., Vol. 5, No. 1 (1959), pp. 25-33, alternative link. %t A307114 Select[Range@500000, DivisorSigma[1, #] > 4 # && Times @@ Boole@ Map[DivisorSigma[1, #] < 4 # &, Most@ Divisors@ #] == 1 &] (* after _Michael De Vlieger_ at A071395 *) %Y A307114 Cf. A000203, A068404, A071395. %K A307114 nonn %O A307114 1,1 %A A307114 _Amiram Eldar_, Mar 25 2019 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE