OFFSET
1,4
COMMENTS
Quetian Superfactorization proceeds by factoring a natural number to its unique prime-exponent factorization (p1^e1 * p2^e2 * ... pj^ej) and then factoring recursively each of the (nonzero) exponents in similar manner, until unity-exponents are finally encountered.
LINKS
FORMULA
EXAMPLE
a(64) = 3, as 64 = 2^6 = 2^(2^1*3^1) and there are three non-1 nodes in that superfactorization. Similarly, for 360 = 2^(3^1) * 3^(2^1) * 5^1 we get a(360) = 5. a(65536) = a(2^(2^(2^(2^1)))) = 4.
MAPLE
a:= proc(n) option remember; `if`(n=1, 0,
add(1+a(i[2]), i=ifactors(n)[2]))
end:
seq(a(n), n=1..100); # Alois P. Heinz, Nov 07 2014
MATHEMATICA
a[n_] := a[n] = If[n == 1, 0, Sum[1 + a[i[[2]]], {i, FactorInteger[n]}]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Nov 11 2015, after Alois P. Heinz *)
PROG
(Scheme, with memoization-macro definec)
(definec (A106490 n) (if (= 1 n) 0 (+ 1 (A106490 (A067029 n)) (A106490 (A028234 n))))) ;; Antti Karttunen, Mar 23 2017
(PARI)
A067029(n) = if(n<2, 0, factor(n)[1, 2]);
A028234(n) = my(f = factor(n)); if (#f~, f[1, 1] = 1); factorback(f); /* after Michel Marcus */
for(n=1, 150, print1(a(n), ", ")) \\ Indranil Ghosh, Mar 23 2017, after formula by Antti Karttunen
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 09 2005 based on Leroy Quet's message ('Super-Factoring' An Integer) posted to SeqFan-mailing list on Dec 06 2003.
STATUS
approved