OFFSET
1,1
COMMENTS
Among the first 1600 multiperfect numbers, there is only one term x for which A007949(x) > A007814(x), and that is x = 6088728021160320, a 4-perfect number, while there are none for which A112765(x) > A007814(x). Only 1, 6, 120, 30240 (incidentally, the first four terms of A007539) seem to be in A025487.
The abundancy index (sigma(n)/n) of the 18 initial terms is: 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 7, 6, 8.
EXAMPLE
459818240 = 2^8 * 5 * 7 * 19 * 37 * 73 is included because while it is a multiple of 5, it is not a multiple of 3.
41254809330254618094796800000 = 2^19 * 3^4 * 5^5 * 7^3 * 11^3 * 13 * 19 * 31^3 * 37 * 41 * 61 is included, because the exponent of 5 (which is 5), is larger than the exponent of 3, which is 4.
MATHEMATICA
mp = Cases[Import["https://oeis.org/A007691/b007691.txt", "Table"], {_, _}][[;; , 2]]; Select[mp, IntegerExponent[#, 5] > IntegerExponent[#, 3] &] (* Amiram Eldar, Nov 30 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 30 2021
STATUS
approved