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).

27720, 50400, 75600, 85680, 95760, 105840, 115920, 120120, 128520, 141120, 143640, 176400, 180180, 184800, 205920, 207900, 214200, 218400, 235620, 239400, 264600, 289800, 292320, 299880, 308880, 312480, 314160, 351120, 371280, 372960, 414960, 425040, 438480

Offset

1,1

Comments

Analogous to A071395 with abundancy index 4 instead of 2.

References

Paul Erdős and János Surányi, Topics in the Theory of Numbers, New York: Springer, 2003, p. 243.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Graeme L. Cohen, Primitive alpha-abundant numbers, Mathematics of Computation, Vol. 43, No. 167 (1984), pp. 263-270.

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.

Paul Erdős, Remarks on number theory. I: On primitive alpha-abundant numbers, Acta Arithmetica., Vol. 5, No. 1 (1959), pp. 25-33, alternative link.

Mathematica

Select[Range@500000, DivisorSigma[1, #] > 4 # && Times @@ Boole@ Map[DivisorSigma[1, #] < 4 # &, Most@ Divisors@ #] == 1 &] (* after Michael De Vlieger at A071395 *)

Crossrefs

Cf. A000203, A068404, A071395.

Sequence in context: A190111 A068404 A279091 * A291458 A023943 A210161

Adjacent sequences: A307111 A307112 A307113 * A307115 A307116 A307117

Keyword

nonn

Author

Amiram Eldar, Mar 25 2019

Status

approved