A327160 - OEIS

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A327160

Number of positive integers that are reachable from n with some combination of transitions x -> usigma(x)-x and x -> gcd(x,usigma(x)), where usigma is the sum of unitary divisors of n (A034448).

1, 2, 2, 2, 2, 1, 2, 2, 2, 4, 2, 4, 2, 5, 4, 2, 2, 6, 2, 5, 3, 6, 2, 5, 2, 4, 2, 5, 2, 4, 2, 2, 5, 6, 3, 6, 2, 7, 3, 6, 2, 4, 2, 4, 5, 5, 2, 7, 2, 7, 5, 8, 2, 4, 3, 4, 3, 4, 2, 1, 2, 7, 3, 2, 3, 4, 2, 7, 4, 8, 2, 7, 2, 7, 3, 6, 3, 3, 2, 7, 2, 6, 2, 7, 3, 6, 6, 7, 2, 1, 5, 6, 4, 8, 4, 9, 2, 9, 5, 9, 2, 4, 2, 7, 7

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OFFSET

1,2

COMMENTS

Question: Is this sequence well defined for every n ? If A318882 is not well defined in whole N, then neither this can be.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

EXAMPLE

From n = 30 we can reach any of the following strictly positive numbers: 30 (e.g., with an empty sequence of transitions), 42 (as A034460(30) = 42), 54 (as A034460(42) = 54; note that A034460(54) = 30 again) and 6 as A323166(30) = A323166(42) = A323166(54) = 6 = A323166(6) = A034460(6), thus a(30) = 4.

PROG

(PARI)

A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448

A327160aux(n, xs) = if(vecsearch(xs, n), xs, xs = setunion([n], xs); if(1==n, xs, my(a=A034448(n)-n, b=gcd(A034448(n), n)); xs = A327160aux(a, xs); if((a==b), xs, A327160aux(b, xs))));

A327160(n) = length(A327160aux(n, Set([])));

CROSSREFS

Cf. A034448, A034460, A318882, A323166.

Cf. also A326198, A327161.

Sequence in context: A063982 A374900 A318882 * A355832 A055020 A052435

Adjacent sequences: A327157 A327158 A327159 * A327161 A327162 A327163

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 25 2019

STATUS

approved