A076763 -id:A076763 - cp's OEIS frontend

A189936 Odd numbers in A076763.

105, 165, 195, 255, 273, 315, 345, 357, 385, 399, 465, 483, 525, 555, 585, 627, 663, 693, 705, 735, 765, 777, 795, 897, 915, 957, 975, 1005, 1095, 1113, 1155, 1173, 1185, 1281, 1295, 1305, 1353, 1365, 1515, 1545, 1575, 1617, 1677, 1683, 1725, 1755, 1785, 1815, 1935, 1953

Offset: 1

Juri-Stepan Gerasimov, May 01 2011

nonn

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A001221, A076763, A013590, A118678, A154430.

omega := proc(n) nops( numtheory[factorset](n)) ; end proc:
isA076763 := proc(n) omega(n) > omega(n-1) and omega(n) > omega(n+1) ; end proc:
isA189936 := proc(n) type(n,'odd') and isA076763(n) ; end proc:
for n from 1 to 2000 by 2 do if isA189936(n) then printf("%d,",n) ; end if; end do;  # R. J. Mathar, May 26 2011

Select[Range[1, 2000, 2], PrimeNu[# - 1] < PrimeNu[#] > PrimeNu[# + 1]&] (* Jean-François Alcover, Nov 14 2016 *)
Select[#[[2,1]]&/@Select[Partition[Table[{n,PrimeNu[n]},{n,2000}],3,1], #[[1,2]] <#[[2,2]]>#[[3,2]]&],OddQ] (* Harvey P. Dale, Sep 15 2019 *)

a(n) = A005408(k) = A076763(m).

Corrected by R. J. Mathar, May 26 2011

A101934 Numbers n with omega(n) smaller than omega(n-1) and omega(n+1).

Original entry on oeis.org

11, 13, 19, 23, 25, 27, 29, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 131, 137, 139, 149, 151, 155, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 221, 223, 227

Offset: 1

Neil Fernandez, Dec 21 2004

			125 is in the sequence because it has one unique prime factor (5), which is fewer than its neighbors 124 (two such factors, namely 2 and 31) and 126 (two such factors, namely 2 and 53).

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A001221, A101932, A076763.

For[i=2, i<1000, If[And[Length[FactorInteger[i 1]]>Length[FactorInteger[i]], Length[FactorInteger[i+1]] > Length[FactorInteger[i]]], Print[i]];i++ ]
(* Second program: *)
Select[Range[1000], PrimeNu[#] < Min[PrimeNu[#-1], PrimeNu[#+1]]&] (* Jean-François Alcover, Nov 14 2016 *)
Flatten[Position[Partition[PrimeNu[Range[250]],3,1],?(#[[1]]>#[[2]]<#[[3]]&),1,Heads->False]]+1 (* _Harvey P. Dale, Apr 18 2021 *)

A101937 Numbers n with omega(n) > omega of 2 nearest larger and 2 nearest smaller neighbors.

Original entry on oeis.org

6, 30, 42, 60, 66, 70, 78, 84, 90, 102, 105, 110, 114, 120, 126, 150, 165, 174, 186, 190, 195, 198, 204, 210, 234, 246, 252, 255, 270, 273, 276, 290, 294, 300, 315, 318, 322, 330, 336, 345, 354, 357, 360, 385, 390, 396, 399, 402, 414, 420

Offset: 1

Neil Fernandez, Dec 21 2004

Prime factors counted without multiplicity. - Harvey P. Dale, Dec 17 2014

			150 is in the sequence because it has three unique prime factors (2,3 and 5), whereas 148, 149, 151 and 152 each have fewer.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A001221, A076763.

For[i=2, i<1000, If[And[Length[FactorInteger[i-2]]{a,b,d,e}]; Flatten[Position[ Partition[ PrimeNu[Range[500]],5,1],?(gr3Q[#]&)]]+2 (* _Harvey P. Dale, Dec 17 2014 *)

A101939 Numbers n with omega(n) > omega of 3 nearest larger and 3 nearest smaller neighbors.

Original entry on oeis.org

6, 30, 42, 60, 66, 70, 78, 84, 90, 110, 114, 120, 126, 150, 174, 186, 190, 204, 210, 246, 290, 294, 300, 322, 330, 336, 385, 390, 414, 420, 450, 462, 510, 540, 546, 570, 630, 660, 690, 714, 720, 770, 780, 786, 798, 840, 846, 858, 870, 910

Offset: 1

Neil Fernandez, Dec 21 2004

			6 is in the sequence because it has two unique prime factors (2 and 3) whereas 3, 4, 5, 7, 8 and 9 each have fewer.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A001221, A076763, A101937.

For[i=3, i<1000, If[And[Length[FactorInteger[i-3]] < Length[FactorInteger[i]], Length[FactorInteger[i-2]] < Length[FactorInteger[i]], Length[FactorInteger[i-1]] < Length[FactorInteger[i]], Length[FactorInteger[i+1]] < Length[FactorInteger[i]], Length[FactorInteger[i+2]] < Length[FactorInteger[i]], Length[FactorInteger[i+3]] < Length[FactorInteger[i]]], Print[i]]; i++]
Clear[noQ];noQ[n_]:=And@@(#?noQ]]+ 3 (* _Harvey P. Dale, Mar 05 2012 *)
Select[Range[650], PrimeNu[#] > Max[PrimeNu[# - 1], PrimeNu[# - 2], PrimeNu[# - 3], PrimeNu[# + 1], PrimeNu[# + 2], PrimeNu[# + 3]] &] (* G. C. Greubel, May 21 2017 *)

cp's OEIS Frontend

A189936 Odd numbers in A076763.

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A101934 Numbers n with omega(n) smaller than omega(n-1) and omega(n+1).

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A101937 Numbers n with omega(n) > omega of 2 nearest larger and 2 nearest smaller neighbors.

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A101939 Numbers n with omega(n) > omega of 3 nearest larger and 3 nearest smaller neighbors.

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