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A260985
Numbers k such that A001222(k) - A001221(k) is an odd prime.
1
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
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
Subsequence of A013929.
Subsequences: A195087, A195089, A195091.
Sequence in context: A223440 A223402 A373286 * A322448 A374588 A354181
KEYWORD
nonn,easy
AUTHOR
STATUS
approved