A088542 - OEIS

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

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OFFSET

1,1

COMMENTS

Also primes p such that the number of prime factors (with repetition) of p! is a multiple of the number of different prime factors of p! (Prime numbers in A088533).

LINKS

Table of n, a(n) for n=1..15.

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

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 *)

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 A333132

Adjacent sequences: A088539 A088540 A088541 * A088543 A088544 A088545

KEYWORD

nonn,hard,more

AUTHOR

Cino Hilliard, Nov 16 2003

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

STATUS

approved