A340302 Numbers k such that k and the least number that is larger than k and has the same prime signature as k also has the same set of distinct prime divisors as k.

12, 72, 144, 420, 432, 540, 864, 1728, 1800, 2000, 2268, 2520, 2592, 5184, 5400, 6300, 7020, 10125, 10368, 10692, 10800, 11340, 12600, 15120, 15552, 16200, 17640, 20000, 20736, 21168, 21600, 24000, 24948, 25200, 26460, 31104, 37800, 40500, 41472, 42750, 43200

Offset

1,1

Comments

Numbers k such that A007947(k) = A007947(A081761(k)).

This sequence is infinite since it includes all the numbers of the form 2*6^k for k>=1.

Links

Amiram Eldar, Table of n, a(n) for n = 1..500

Index entries for sequences related to prime signature

Example

12 = 2^2 * 3 is a term since the least number that is larger than 12 and has the same prime signature as 12 is 18 = 2 * 3^2 which also has the same set of distinct prime divisors as 12, {2, 3}.

Mathematica

sig[n_] := Sort@FactorInteger[n][[;; , 2]]; nextsig[n_] := Module[{sign = sig[n], k = n + 1}, While[sig[k] != sign, k++]; k]; rad[n_] := Times @@ FactorInteger[n][[;; , 1]]; Select[Range[2, 1000], rad[#] == rad[nextsig[#]] &]

Crossrefs

Cf. A007947, A081761, A085079, A089247, A118914, A167747.

Sequence in context: A219302 A338261 A101523 * A143698 A304164 A199531

Adjacent sequences: A340299 A340300 A340301 * A340303 A340304 A340305

Keyword

nonn

Author

Amiram Eldar, Jan 03 2021

Status

approved