A088542 Prime numbers p such that A022559(p) is a multiple of A000720(p).
2, 3, 7, 71, 179, 547, 983, 1283, 1289, 2909, 3709, 20269, 40829, 256579, 772573
Offset: 1
Examples
A022559(7) = 8 is a multiple of A000720(7) = 4.
Programs
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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 Select[Prime[Range[530]],Divisible[PrimeOmega[#!],PrimeNu[#!]]&] (* The program generates the first 11 terms of the sequence. To generate more, increase the Range constant, but the program will then take a long time to run. *) (* Harvey P. Dale, Jan 01 2020 *) -
PARI
for(x=2,10000,x1=x!;y=bigomega(x1)/omega(x1); if(y==floor(y),if(isprime(x), print1((x)","))))
Extensions
Edited and extended by Stefan Steinerberger, Dec 11 2007
Offset corrected by Mohammed Yaseen, Jul 20 2023
a(14)-a(15) from Alois P. Heinz, Jul 20 2023
Comments