A385209 - OEIS

A385209

Least k such that A086369(k) = n.

1, 2, 3, 4, 9, 6, 15, 16, 81, 12, 45, 64, 729, 24, 105, 36, 225, 48, 405, 1024, 59049, 60, 315, 4096, 531441, 192, 3645, 144, 2025, 120, 945, 65536, 43046721, 180, 1575, 262144, 387420489, 240, 2835, 576, 18225, 3072, 295245, 4194304, 31381059609, 360, 3465, 1296

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OFFSET

1,2

COMMENTS

A086369(n) is also the cardinality of the set containing the divisors d of n and those 0 < m < n satisfying m + d = n.

LINKS

Table of n, a(n) for n=1..48.

FORMULA

a(2*p-1) = 3^(p-1) for prime p. - Jinyuan Wang, Jun 30 2025

EXAMPLE

a(4) = 4 since 4 is the least k such that A086369(k) = 4.

a(13) = 729 since 729 is the least k such that A086369(k) = 13.

PROG

(PARI) a(n, k) = my(f); (f(n) = if(n%2==1, 1+2*sumdiv(n, d, d<n/2), 2+2*sumdiv(n, d, d<n/2))); for(m=1, k, if(f(m)==n, return(m), 0)) \\ k defines the length of the search, returns 0 if n is not found

CROSSREFS

Cf. A086369, A385202.

Sequence in context: A060866 A064478 A111798 * A375015 A249543 A307404

Adjacent sequences: A385206 A385207 A385208 * A385210 A385211 A385212

KEYWORD

nonn

AUTHOR

Miles Englezou, Jun 21 2025

EXTENSIONS

a(45)-a(48) from Jinyuan Wang, Jun 30 2025

STATUS

approved