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A253630 Number of iterations of A253629 needed for n to reach 2. 1
0, 2, 1, 3, 2, 3, 2, 4, 3, 4, 3, 4, 3, 5, 3, 5, 4, 5, 4, 5, 4, 5, 4, 6, 4, 6, 4, 6, 5, 5, 4, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 7, 5, 6, 5, 6, 6, 7, 5, 7, 6, 7, 5, 7, 6, 7, 6, 6, 5, 7, 5, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 8, 6, 7, 6, 7, 6, 8, 6, 7, 6, 8, 6, 8, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

If x or y is odd, then a(xy) = a(x) + a(y).

If x and y are both even, then a(xy) = a(x) + a(y) + 1.

Equivalently, if we define a function D by D(x) = a(x) if x is odd and D(x) = a(x) + 1 if x is even, then D is completely additive.

LINKS

Table of n, a(n) for n=2..88.

Colin Defant, An arithmetic function arising from the Dedekind psi function, arXiv:1501.00971 [math.NT], 2015.

MATHEMATICA

L[n_] := If[EvenQ[n], (1/3) If[n > 1, n Times @@ (1 + 1/(Select[Divisors[n], PrimeQ])), 1], If[n > 1, n Times @@ (1 + 1/(Select[Divisors[n], PrimeQ])), 1]]; Table[Length@NestWhileList[L, n, # != 1 &] - 2, {n, 2, 260}]

PROG

(PARI) a253629(n) = my(f=factor(n)); prod(i=1, #f~, f[i, 1]^(f[i, 2]-1)*if(f[i, 1]>2, f[i, 1]+1, 1)) ;

a(n) = my(nb = 0); my(m = n); while(m != 2, m = a253629(m); nb++); nb; \\ Michel Marcus, Jan 21 2015

CROSSREFS

Cf. A253629.

Sequence in context: A070804 A303429 A303656 * A104481 A078709 A023022

Adjacent sequences:  A253627 A253628 A253629 * A253631 A253632 A253633

KEYWORD

nonn

AUTHOR

Colin Defant, Jan 06 2015

STATUS

approved

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Last modified March 3 04:22 EST 2021. Contains 341756 sequences. (Running on oeis4.)