[go: up one dir, main page]

login
A078174
Numbers with an integer arithmetic mean of distinct prime factors.
34
2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37, 39, 41, 42, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 64, 65, 67, 69, 71, 73, 75, 77, 78, 79, 81, 83, 84, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 110, 111, 113, 114, 115
OFFSET
1,1
COMMENTS
A008472(a(n)) == 0 modulo A001221(a(n)).
LINKS
FORMULA
a(n) << n log n/(log log n)^k for any k. - Charles R Greathouse IV, May 30 2013
EXAMPLE
42=2*3*7: (2+3+7)/3=4, therefore 42 is a term.
MATHEMATICA
Select[Range[2, 200], IntegerQ[Mean[Transpose[FactorInteger[#]][[1]]]]&] (* Harvey P. Dale, Apr 18 2016 *)
PROG
(PARI) is(n)=my(f=factor(n)[, 1]); sum(i=1, #f, f[i])%#f==0 \\ Charles R Greathouse IV, May 30 2013
(Haskell)
a078174 n = a078174_list !! (n-1)
a078174_list = filter (\x -> a008472 x `mod` a001221 x == 0) [2..]
-- Reinhard Zumkeller, Jun 01 2013
CROSSREFS
Union of A000961 and A070005.
Positions of 1's in A323172.
The version counting multiplicity is A078175.
The version for prime indices is A326621.
The average of the set of distinct prime factors is A323171/A323172.
The average of the multiset of prime factors is A123528/A123529.
Sequence in context: A213715 A360552 A373852 * A174894 A275616 A088948
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Nov 20 2002
STATUS
approved