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
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
Programs
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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);
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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
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