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 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. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 1 23:26 EST 2023. Contains 367503 sequences. (Running on oeis4.)