A105402 Positive integers k such that the prime factors of sigma(k) are a subset of the prime factors of k.

1, 6, 28, 30, 42, 66, 84, 102, 120, 138, 186, 210, 270, 282, 318, 330, 364, 420, 426, 462, 496, 510, 546, 570, 642, 672, 690, 714, 762, 840, 868, 870, 924, 930, 966, 1080, 1092, 1122, 1146, 1302, 1320, 1410, 1428, 1488, 1518, 1590, 1638, 1722, 1770, 1782, 1890

Offset

1,2

Comments

Also numbers k such that k^k/sigma(k) is integral. - Vicente Izquierdo Gomez, Jan 04 2013.

Pollack and Pomerance call these numbers "prime-deficient numbers". - Amiram Eldar, Jun 02 2020

Links

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

Paul Pollack and Carl Pomerance, Prime-Perfect Numbers, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 12a, Paper A14, 2012.

Example

102 is a term since 102 = 2*3*17 and sigma(102) = 2^3*3^3.

Maple

A:=select(proc(z) numtheory[factorset](sigma(z)) subset numtheory[factorset](z) end, [$1..100000]); has 716 members.

Mathematica

Select[Range[2000], IntegerQ[#^#/DivisorSigma[1, #]] &] (* Vicente Izquierdo Gomez, Jan 04 2013 *)

Crossrefs

Cf. A000203, A027598, A058063, A054027, A014567, A023194, A175200.

Sequence in context: A342922 A389463 A357462 * A362805 A145551 A356410

Adjacent sequences: A105399 A105400 A105401 * A105403 A105404 A105405

Keyword

easy,nonn

Author

Walter Kehowski, May 01 2005

Extensions

Extended by R. J. Mathar, Dec 08 2008

Status

approved