A242965 Numbers whose anti-divisors are all primes.

3, 4, 5, 7, 8, 11, 16, 17, 19, 29, 43, 47, 61, 64, 71, 79, 89, 101, 107, 109, 151, 191, 197, 223, 251, 271, 317, 349, 359, 421, 439, 461, 521, 569, 601, 631, 659, 673, 691, 701, 719, 811, 821, 881, 911, 919, 947, 971, 991, 1009, 1024, 1051, 1091, 1109, 1153

Offset: 1

Author

Paolo P. Lava, May 28 2014

Keywords

• nonn
• easy

Examples

			The anti-divisors of 191 are all primes: 2, 3, 127.
The same for 1024: 3, 23, 89, 683.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A066272, A242966.

Programs

Maple

P := proc(q) local k,ok,n; for n from 3 to q do ok:=1;
for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then
if not isprime(k) then ok:=0; break; fi; fi; od;
if ok=1 then print(n); fi; od; end: P(10^3);

Python

from sympy import divisors, isprime
for n in range(3, 10**4):
    for d in [2*d for d in divisors(n) if n > 2*d and n % (2*d)] + \
             [d for d in divisors(2*n-1) if n > d >= 2 and n % d] + \
             [d for d in divisors(2*n+1) if n > d >= 2 and n % d]:
        if not isprime(d):
            break
    else:
        print(n, end=', ')
# Chai Wah Wu, Aug 15 2014