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

Author

Walter Kehowski, May 01 2005

Keywords

• easy
• nonn

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

Examples

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

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.

Crossrefs

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

Programs

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 *)

Extensions

Extended by R. J. Mathar, Dec 08 2008