A195091 -id:A195091 - cp's OEIS frontend

A195093 Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 9.

1024, 3072, 4608, 5120, 6912, 7168, 10368, 11264, 12800, 13312, 15360, 15552, 17408, 19456, 21504, 23040, 23328, 23552, 25088, 29696, 31744, 32000, 32256, 33792, 34560, 34992, 35840, 37888, 38400, 39936, 41984, 44032, 48128, 48384

Offset: 1

Harvey P. Dale, Sep 08 2011

The asymptotic density of this sequence is (6/Pi^2) * Sum_{k>=1} f(a(k)) = 0.0007396..., where f(k) = A112526(k) * Product_{p|k} p/(p+1). - Amiram Eldar, Sep 24 2024

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences computed from exponents in factorization of n.

Cf. A060687, A195069, A195086, A195087, A195088, A195089, A195090, A195091, A195092.

Cf. A025487, A046660, A059956, A112526, A257851, A261256, A264959.

a195093 n = a195093_list !! (n-1)
a195093_list = filter ((== 9) . a046660) [1..]
-- Reinhard Zumkeller, Nov 29 2015

Select[Range[50000],PrimeOmega[#]-PrimeNu[#]==9&]

is(n)=bigomega(n)-omega(n)==9 \\ Charles R Greathouse IV, Sep 14 2015

A046660(a(n)) = 9. - Reinhard Zumkeller, Nov 29 2015

A260985 Numbers k such that A001222(k) - A001221(k) is an odd prime.

Original entry on oeis.org

16, 48, 64, 72, 80, 81, 108, 112, 162, 176, 192, 200, 208, 240, 256, 272, 288, 304, 320, 336, 360, 368, 392, 405, 432, 448, 464, 496, 500, 504, 528, 540, 560, 567, 592, 600, 624, 625, 648, 656, 675, 688, 704, 729, 752, 756, 768, 792, 800, 810, 816, 832, 848

Offset: 1

Carlos Eduardo Olivieri, Aug 06 2015

The asymptotic density of this sequence is (6/Pi^2) * Sum_{k>=1} f(a(k)) = 0.0626525..., where f(k) = A112526(k) * Product_{p|k} p/(p+1). - Amiram Eldar, Sep 24 2024

			16 is in the sequence because A001222(16) - A001221(16) = 3.
80 is in the sequence because A001222(80) - A001221(80) = 3.
192 is in the sequence because A001222(192) - A001221(192) = 5.

Cf. A001221, A001222, A046660, A059956, A112526.
Subsequence of A013929.
Subsequences: A195087, A195089, A195091.

Select[Range[10^3], !PrimeQ[#] && PrimeQ[p = PrimeOmega[#] - PrimeNu[#]] && OddQ[p] &]

isok(n) = (d=bigomega(n)-omega(n)) && (d != 2) && isprime(d); \\ Michel Marcus, Aug 07 2015

from sympy import isprime, primefactors
def omega(n): return 0 if n==1 else len(primefactors(n))
def bigomega(n): return 0 if n==1 else bigomega(n//min(primefactors(n))) + 1
def ok(n):
    d = bigomega(n) - omega(n)
    return d%2 and isprime(d)
print([n for n in range(1, 1001) if ok(n)]) # Indranil Ghosh, Apr 25 2017

cp's OEIS Frontend

A195093 Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 9.

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