A376384 - OEIS

A376384

Numbers k such that there exists at least two m <= k such that both rad(m) | k and m is neither squarefree nor a prime power, i.e., m is in A126706, where rad = A007947.

18, 24, 30, 36, 40, 42, 48, 50, 54, 56, 60, 66, 70, 72, 75, 78, 80, 84, 88, 90, 96, 98, 100, 102, 104, 105, 108, 110, 112, 114, 120, 126, 130, 132, 135, 136, 138, 140, 144, 147, 150, 152, 154, 156, 160, 162, 165, 168, 170, 174, 176, 180, 182, 184, 186, 189, 190

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OFFSET

1,1

COMMENTS

Numbers k such that A376505(k) > 1. A376505(k) >= 1 for all k in A126706.

Numbers k such that the cardinality of the intersection of row n of A162306 and A126706 exceeds 1.

Excludes prime powers; subsequence of A024619.

a(n) is not in A366825, since for k in A366825, there is only one m <= k that is in A126706, and that is k itself.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Hasse diagrams of row a(n) of A162306 for n = 1..12, showing numbers m in A126706 in blue, primes in red, perfect prime powers in gold, and squarefree composites in green.

FORMULA

a(n) = card({ m <= a(n) : rad(m) | a(n), Omega(m) > omega(m) > 1 }), where Omega = A001222 and omega = A001221.

EXAMPLE

Table showing the intersection of A126706 and row a(n) of A162306 for n = 1..12:

18: {12, 18},

24: {12, 18, 24},

30: {12, 18, 20, 24},

36: {12, 18, 24, 36},

40: {20, 40},

42: {12, 18, 24, 28, 36},

48: {12, 18, 24, 36, 48},

50: {20, 40, 50},

54: {12, 18, 24, 36, 48, 54},

56: {28, 56},

60: {12, 18, 20, 24, 36, 40, 45, 48, 50, 54, 60},

66: {12, 18, 24, 36, 44, 48, 54}.

MATHEMATICA

Select[Range[2^8], Function[n, 1 < Count[Range[n], _?(And[Divisible[n, Times @@ FactorInteger[#][[All, 1]]], Nor[SquareFreeQ[#], PrimePowerQ[#]]] &)] ] ]

CROSSREFS

Cf. A000961, A001221, A001222, A005117, A007947, A024619, A126706, A162306.

Sequence in context: A076770 A105679 A160810 * A076771 A375162 A179014

Adjacent sequences: A376381 A376382 A376383 * A376385 A376386 A376387

KEYWORD

nonn,easy

AUTHOR

Michael De Vlieger, Oct 02 2024

STATUS

approved