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%I #33 May 03 2024 14:25:05
%S 1,2,4,6,10,11,12,16,18,22,23,28,29,30,35,36,39,40,42,44,46,47,52,55,
%T 58,59,60,62,66,69,70,71,72,78,79,82,83,88,89,95,96,100,102,104,106,
%U 107,108,111,112,119,125,126,130,131,134,136,138,139,143,148,149,150,153
%N Indices n of terms of sequence A001142, Product_{k=0..n} binomial(n,k), that are divisible by all primes <= n.
%C a(n) + 1 is either a prime or a "mutinous number" (A027854).
%H Michael De Vlieger, <a href="/A056077/b056077.txt">Table of n, a(n) for n = 1..10000</a>
%H Hans Montanus and Ron Westdijk, <a href="https://greenbluemath.nl/wp-content/uploads/2024/03/Cellular-Automation-and-Binomials.pdf">Cellular Automation and Binomials</a>, Green Blue Mathematics (2022), p. 69.
%F 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
%e 11 is included because Product_{k=0..11} binomial(11, k) is divisible by 2, 3, 5, 7 and 11.
%p isA056077 := proc(n) local radh; radh := proc(n) option remember;
%p mul(k, k = numtheory:-factorset(mul(k^k/factorial(k), k=0..n))) end;
%p type(radh(n)/radh(n-1), integer) end: # isA056077(0) = true.
%p select(isA056077, [$1..153]); # _Peter Luschny_, Dec 21 2019
%t 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 *)
%Y Cf. A001142, A056606, A027854, A002110.
%K easy,nonn
%O 1,2
%A _Leroy Quet_, Jul 26 2000
%E Extended by _Ray Chandler_, Nov 17 2008
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