A347242 Numbers k such that when iterating the map x -> A000593(x), then at some point before 1 is reached (after starting from x=k), a term is encountered whose largest prime factor is at least as large as A006530(k).

9, 18, 25, 27, 36, 45, 49, 50, 54, 55, 63, 72, 75, 81, 90, 98, 99, 100, 108, 110, 117, 121, 125, 126, 135, 144, 147, 150, 162, 165, 169, 175, 180, 196, 198, 200, 216, 220, 225, 234, 242, 243, 245, 250, 252, 270, 275, 288, 289, 294, 300, 315, 324, 325, 330, 338, 343, 350, 360, 361, 363, 375, 385, 392, 396, 400

Offset

1,1

Comments

Provided there does not exist any odd perfect numbers, then these are numbers k for which A347240(k) >= A006530(k), as for any odd perfect number x, A347240(x) = -1 by its escape clause.

If k is included as a term, then also 2*k is present.

Not all odd squares of primes are present. For example 67^2 and 79^2 are not included. See also A091490 that seems to be a subsequence of those exceptions.

Conjecture: There are no primes in this sequence. Checked up to the 2^20-th prime, 16290047.

Links

Table of n, a(n) for n=1..66.

Index entries for sequences where odd perfect numbers must occur, if they exist at all

Example

For n = 55 = 5*11, on the first iteration we get A000593(55) = 72 = 2^3 * 3^2, but both 2 and 3 are less than 11, therefore, we iterate second time, to get A000593(72) = 13, which is the first where the largest prime factor is larger than that of 55 (13 > 11), thus 55 is included in the sequence.

Prog

(PARI)
A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
A000265(n) = (n >> valuation(n, 2));
A000593(n) = sigma(A000265(n));
A347244(n) = { my(gpf=A006530(n)); while(n>1, n = A000593(n); if(A006530(n)>=gpf, return(1))); (0); };
isA347242(n) = A347244(n);

Crossrefs

Cf. A000593, A006530, A091490, A161942, A336353, A336361, A347240, A347241, A347243 (complement), A347244 (characteristic function).

Positions of nonzero terms in A347245.

Sequence in context: A015798 A028494 A167663 * A038838 A347247 A038837

Adjacent sequences: A347239 A347240 A347241 * A347243 A347244 A347245

Keyword

nonn

Author

Antti Karttunen, Aug 28 2021

Status

approved