Errata for : L. Alaoglu , Erd"os P'al = Paul Erdos On Highly Composite and Similar Numbers Transactions of the American Math. Society , 1944 Nov , V56#3pp448-469 http://links.jstor.org/sici?sici=0002.9947(194411)56:3<448:OHCASN>2.0.CO;2.S http://www.jstor.org/stable/1990319 http://www.renyi.hu/~p_erdos/1944-03.pdf In the table of SUPERABUNDANT NUMBERS LESS THAN 10 to the 18th on p. 468 : in line 27 for 4.368 read 4.363 in line 38 = top of the rightmore segment with abundancy 4.855 for 3 to the 2 read 3 to the 3 Note that correct data for 3 to the 2 already appears in line 35 . Note that the abundancies in the table are truncated , not rounded . Not to be so obscure about it , the superabundant numbers concerned and their abundancies are : 332640 = 2^5 * 3^3 * 5 * 7 * 11 4.36363636 7207200 = 2^5 * 3^2 * 5^2 * 7 * 11 * 13 4.73454545 21621600 = 2^5 * 3^3 * 5^2 * 7 * 11 * 13 4.85594406 All other values in this table have been verified . Other comments and errata for this article can be found on pp. 67-68 of Erd"os P'al = Paul Erdos , Jean-Louis Nicolas R'epartition des Nombres Superabondants = Repartition des Nombres Superabondants Bulletin de la Soci'et'e Math'ematique de France , 1975 , V103#1pp65-90 Bulletin de la Societe Mathematique de France , 1975 , V103#1pp65-90 http://www.renyi.hu/~p_erdos/1975-37.pdf --- Errata for : Erd"os P'al = Paul Erdos , Jean-Louis Nicolas R'epartition des Nombres Superabondants = Repartition des Nombres Superabondants Bulletin de la Soci'et'e Math'ematique de France , 1975 , V103#1pp65-90 Bulletin de la Societe Mathematique de France , 1975 , V103#1pp65-90 http://www.renyi.hu/~p_erdos/1975-37.pdf On p. 89 : for 42336(85/28); 45864(85/28) read 42336(95/28); 45864(95/28)
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2000 Mathematics Subject Classification : Primary 11A25 ; Secondary 11A05 , 11A41 , 11A51 , 11N05 , 11N25 , 11Y05 , 11Y11 , 11Y55 .
Walter Nissen
2009-09-29