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 A088542 Prime numbers n such that A022559(n) is a multiple of A000720(n). 0
 2, 3, 7, 71, 179, 547, 983, 1283, 1289, 2909, 3709, 20269, 40829 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Also primes n such that the number of prime factors (with repetition) of n! is a multiple of the number of different prime factors of n! (Prime numbers in A088533). LINKS EXAMPLE A022559(7) = 8 is a multiple of A000720(7) = 4. MATHEMATICA a = {2}; b = {1}; For[n = 3, n < 1000, n++, If[PrimeQ[n], AppendTo[b, 1], c = FactorInteger[n]; For[j = 1, j < Length[c] + 1, j++, b[[PrimePi[c[[j, 1]]]]] = b[[PrimePi[c[[j, 1]]]]] + c[[j, 2]]]]; If[Mod[Plus @@ b, Length[b]] == 0, If[PrimeQ[n], AppendTo[a, n]]]]; a PROG (PARI) for(x=2, 10000, x1=x!; y=bigomega(x1)/omega(x1); if(y==floor(y), if(isprime(x), print1((x)", ")))) CROSSREFS Cf. A000720, A022559, A088533. Sequence in context: A181263 A130309 A090870 * A075840 A096225 A035094 Adjacent sequences:  A088539 A088540 A088541 * A088543 A088544 A088545 KEYWORD hard,nonn AUTHOR Cino Hilliard (hillcino368(AT)gmail.com), Nov 16 2003 EXTENSIONS Edited and extended by Stefan Steinerberger, Dec 11 2007 STATUS approved

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