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A105402 Positive integers k such that the prime factors of sigma(k) are a subset of the prime factors of k. 5
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A261868 A342922 A357462 * A362805 A145551 A356410
KEYWORD
easy,nonn
AUTHOR
Walter Kehowski, May 01 2005
EXTENSIONS
Extended by R. J. Mathar, Dec 08 2008
STATUS
approved

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Last modified July 17 12:34 EDT 2024. Contains 374377 sequences. (Running on oeis4.)