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.

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

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 A355446 A009785

Adjacent sequences: A340302 A340303 A340304 * A340306 A340307 A340308

Keyword

nonn

Author

Amiram Eldar, Jan 03 2021

Status

approved