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

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

1,1

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..3000

Index entries for sequences computed from exponents in factorization of n.

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A001221, A001222, A046660, A059956, A112526.

Subsequence of A013929.

Subsequences: A195087, A195089, A195091.

Sequence in context: A223440 A223402 A373286 * A322448 A374588 A354181

Adjacent sequences: A260982 A260983 A260984 * A260986 A260987 A260988

Keyword

nonn,easy

Author

Carlos Eduardo Olivieri, Aug 06 2015

Status

approved