

A340305


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


2



12, 45, 60, 63, 84, 132, 156, 175, 204, 228, 275, 276, 315, 325, 348, 350, 372, 420, 425, 444, 475, 492, 495, 516, 525, 539, 540, 564, 575, 585, 636, 637, 660, 675, 693, 700, 708, 732, 765, 780, 804, 819, 833, 852, 855, 876, 924, 931, 948, 996, 1020, 1035, 1068
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OFFSET

1,1


COMMENTS

Numbers k such that k and A065642(k) have the same prime signature (A118914).


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000
Index entries for sequences related to prime signature


EXAMPLE

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


MATHEMATICA

rad[n_] := Times @@ FactorInteger[n][[;; , 1]]; next[n_] := Module[{r = rad[n]}, SelectFirst[Range[n + 1, n^2], rad[#] == r &]]; sig[n_] := Sort @ FactorInteger[n][[;; , 2]]; Select[Range[2, 300], sig[#] == sig[next[#]] &]


CROSSREFS

Cf. A065642, A118914.
Subsequence: A251720.
Sequence in context: A320998 A294521 A309817 * A194284 A009785 A135710
Adjacent sequences: A340302 A340303 A340304 * A340306 A340307 A340308


KEYWORD

nonn


AUTHOR

Amiram Eldar, Jan 03 2021


STATUS

approved



