A048124 Becomes prime or 4 after exactly 2 iterations of f(x) = sum of prime factors of x.

8, 9, 21, 25, 30, 32, 35, 36, 42, 50, 57, 60, 64, 72, 81, 85, 86, 93, 102, 111, 115, 121, 122, 138, 145, 146, 159, 164, 174, 182, 187, 194, 215, 219, 235, 236, 237, 253, 258, 260, 265, 266, 282, 284, 287, 289, 302, 303, 308, 312, 318, 319, 326, 329, 338, 346

Offset

1,1

Comments

f(x) = sum of prime factors with multiplicity, so that f(1500) = 2+2+3+5+5+5 = 22.

Numbers k such that A002217(k) = 3. - Andrew Howroyd, Sep 15 2019

Links

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Mathematica

okQ[n_]:=Module[{lst=NestList[Total[Times@@@FactorInteger[#]]&, n, 2]}, !PrimeQ[First[lst]] &&!PrimeQ[lst[[2]]]&&First[lst]!=4&&lst[[2]]!=4&&(PrimeQ[Last[lst]]||Last[lst]==4)]; Select[Range[400], okQ] (* Harvey P. Dale, Mar 23 2011 *)

Prog

(PARI) sopfr(n)={my(f=factor(n)); sum(i=1, #f~, f[i, 1]*f[i, 2])}
ok(n)={forstep(k=2, 1, -1, n=sopfr(n); if(n==4||isprime(n), return(k==1))); 0}
select(ok, [1..500]) \\ Andrew Howroyd, Sep 14 2019

Crossrefs

Cf. A002217, A048125, A048126, A048127, A048128, A048129, A048130, A048131, A048132.

Sequence in context: A326444 A309484 A308989 * A322637 A322640 A303957

Adjacent sequences: A048121 A048122 A048123 * A048125 A048126 A048127

Keyword

nonn

Author

David W. Wilson

Status

approved