|
|
A056077
|
|
Indices n of terms of sequence A001142, Product_{k=0..n} binomial(n,k), that are divisible by all primes <= n.
|
|
5
|
|
|
1, 2, 4, 6, 10, 11, 12, 16, 18, 22, 23, 28, 29, 30, 35, 36, 39, 40, 42, 44, 46, 47, 52, 55, 58, 59, 60, 62, 66, 69, 70, 71, 72, 78, 79, 82, 83, 88, 89, 95, 96, 100, 102, 104, 106, 107, 108, 111, 112, 119, 125, 126, 130, 131, 134, 136, 138, 139, 143, 148, 149, 150, 153
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
a(n) + 1 is either a prime or a "mutinous number" (A027854).
|
|
LINKS
|
|
|
FORMULA
|
Let h(m) = Product(PrimeDivisors(Product_{k=0..m} k^k/k!)). If h(m-1) divides h(m) then m is in this sequence. # Peter Luschny, Dec 21 2019
|
|
EXAMPLE
|
11 is included because Product_{k=0..11} binomial(11, k) is divisible by 2, 3, 5, 7 and 11.
|
|
MAPLE
|
isA056077 := proc(n) local radh; radh := proc(n) option remember;
mul(k, k = numtheory:-factorset(mul(k^k/factorial(k), k=0..n))) end;
type(radh(n)/radh(n-1), integer) end: # isA056077(0) = true.
|
|
MATHEMATICA
|
With[{s = Select[Range@ 154, Function[n, (n/Apply[Power, Last@ #]) > #[[-1, 1]] &@ FactorInteger[n]]]}, -1 + Union[s, Prime@ Range@ PrimePi@ Max@ s]] (* Michael De Vlieger, Sep 23 2017 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|