A347422 Numbers k such that the product of the number of divisors of k and the number of pairs of primes summing to k is k itself.
24, 36, 72, 1056, 1176, 11232, 226080
Offset: 1
Examples
For 24, the number of divisors is 8 (1, 2, 3, 4, 6, 8, 12, 24), the number of pairs of prime numbers summing to 24 is 3: (5, 19), (7, 17), (11, 13), and 3*8=24, so 24 is a term. Similarly, for 226080, the number of divisors is 72, and the number of pairs of prime numbers summing to 226080 is 3140. And 72*3140 = 226080, so 226080 is a term.
Links
- Anudeex Shetty, Python program for A347422
Programs
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Mathematica
Select[Range[12000], IntegerQ[(r = #/DivisorSigma[0, #])] && r == Length @ IntegerPartitions[#, {2}, Select[Range[#], PrimeQ]] &] (* Amiram Eldar, Sep 02 2021 *) -
PARI
f(n) = my(s); forprime(q=2, n\2, s+=isprime(n-q)); s; \\ A061358 isok(k) = my(x = k/numdiv(k)); (denominator(x)==1) && (f(k) == x); \\ Michel Marcus, Sep 10 2021
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