A157485 -id:A157485 - cp's OEIS frontend

A157486 Numbers n such that n-+1 are divisible by exactly 6 primes, counted with multiplicity.

1889, 3079, 4591, 5023, 6175, 6641, 7649, 9881, 10961, 11501, 11935, 12689, 13751, 14417, 15499, 15713, 16687, 18017, 18089, 18271, 19169, 19249, 19889, 19951

Offset: 1

Vladimir Joseph Stephan Orlovsky, Mar 01 2009

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..4000

Cf. A124936, A014612, A157483, A157484, A157485

q=6;lst={};Do[If[Plus@@Last/@FactorInteger[n-1]==q&&Plus@@Last/@FactorInteger[n+1]==q,AppendTo[lst,n]],{n,9!}];lst
Mean/@SequencePosition[PrimeOmega[Range[20000]],{6,,6}] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale, Sep 23 2019 *)

A157487 Numbers k such that k-1 and k+1 are each the product of exactly 7 primes, counted with multiplicity.

Original entry on oeis.org

10529, 15391, 17983, 18751, 22049, 23489, 24751, 26081, 29249, 32561, 35153, 43471, 49951, 52975, 58049, 58481, 67229, 67231, 70687, 71873, 72415, 76049, 77921, 79001, 79649, 82783, 83249, 85751, 88289, 93799, 95551, 97471, 102545

Offset: 1

Vladimir Joseph Stephan Orlovsky, Mar 01 2009

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..3000

Cf. A124936, A014612, A157483, A157484, A157485, A157486.

with(numtheory): a := proc (n) if bigomega(n-1) = 7 and bigomega(n+1) = 7 then n else end if end proc: seq(a(n), n = 2 .. 120000); # Emeric Deutsch, Mar 07 2009

q=7;lst={};Do[If[Plus@@Last/@FactorInteger[n-1]==q&&Plus@@Last/@FactorInteger[n+1]==q,AppendTo[lst,n]],{n,9!}];lst
Select[Range[110000],PrimeOmega[#+{1,-1}]=={7,7}&] (* Harvey P. Dale, Apr 04 2015 *)
Mean/@SequencePosition[PrimeOmega[Range[105000]],{7,,7}] (* _Harvey P. Dale, Sep 10 2022 *)

More terms from Emeric Deutsch, Mar 07 2009

A157489 Numbers n such that n-+5 are divisible by exactly 5 primes, counted with multiplicity.

Original entry on oeis.org

275, 373, 445, 755, 985, 1165, 1245, 1475, 1535, 1643, 1645, 1705, 1715, 1745, 2219, 2305, 2317, 2389, 2445, 2455, 2543, 2579, 2845, 2855, 2893, 3229, 3299, 3325, 3371, 3565, 3613, 3659, 3695, 3757, 3829, 3875, 4255, 4285, 4295, 4345, 4355, 4477, 4745, 5003, 5065

Offset: 1

Vladimir Joseph Stephan Orlovsky, Mar 01 2009

nonn

Let a, b and 10 be pairwise coprime, with A001222(a) = A001222(b) = 4. There exists c such that c == 5 (mod a) and c == -5 (mod b). Dickson's conjecture implies that (c+k*a*b-5)/a and (c+k*a*b+5)/b are prime for infinitely many k; for such k, c+k*a*b is in the sequence. - Robert Israel, Mar 22 2020

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A001222, A124936, A014612, A157483, A157484, A157485, A157486

N:= 10^4: # for terms <= N
T5:= select(t -> numtheory:-bigomega(t)=5, {$1..N+5}):
S:= T5 intersect map(`+`,T5,10):
sort(convert(map(`-`,S,5),list)); # Robert Israel, Mar 22 2020

q=5;lst={};Do[If[Plus@@Last/@FactorInteger[n-q]==q&&Plus@@Last/@FactorInteger[n+q]==q,AppendTo[lst,n]],{n,8!}];lst
SequencePosition[PrimeOmega[Range[5100]],{5,,,_,,,_,,,_,5}][[All,1]]+5 (* Harvey P. Dale, Sep 23 2021 *)

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A157486 Numbers n such that n-+1 are divisible by exactly 6 primes, counted with multiplicity.

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A157487 Numbers k such that k-1 and k+1 are each the product of exactly 7 primes, counted with multiplicity.

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A157489 Numbers n such that n-+5 are divisible by exactly 5 primes, counted with multiplicity.

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