OFFSET
1,2
COMMENTS
Sequence consists of those positive integers m where, if m = Product_{p prime, p|m} p^k(p), each k(p) = positive integer, then Sum_{p prime, p|m} p^k(p) = twice the largest prime power dividing m. The inclusion of 1 in the sequence is debatable.
There is substantial overlap between the terms here and in A298010, which has a straightforward cause in the two definitions. Initially (looking at the 46 terms currently in the data section) the majority of the terms that are in A298010 but not here are the oblong (a.k.a. pronic) numbers, A002378; and the terms that are here but not in A298010 are in the subsequence A071312, except for the "debatable" 1. The 2nd term not in A071312 or A298010 is 7980. - Peter Munn, Apr 07 2024
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
EXAMPLE
84 = 2^2 * 3 * 7. Now 7 = 2^2 + 3, so 84 is in the sequence.
120 = 2^3 * 3 * 5. Now 2^3 = 3 + 5, so 120 is in the sequence.
MATHEMATICA
f[n_] := Block[{pp}, If[n == 1, Return[True]]; pp = Power @@@ FactorInteger[n]; Return[2Max[pp] == Plus @@ pp]; ]; Select[Range[6500], f] (* Ray Chandler, Dec 04 2005 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Dec 01 2005
EXTENSIONS
Edited by Ray Chandler, Dec 04 2005
STATUS
approved