OFFSET
1,1
COMMENTS
This sequence is interesting because the sequence of any member's divisors increases approximately exponentially, without members having any repeated prime factors.
Removing the limitation a=round(sqrt(b)) results in A261657.
This sequence would be particularly interesting if the b and c of one member were the a and b of another, as it could give us a number with 4 prime factors and similar properties as here. The resulting compound would be a member of A261658. No such pairs exist in this sequence with any lowest factor < 10000.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
The prime factors of 3333 are 3, 11, and 101. 3^4=81, 11^2=121, and the average of 81 and 121 gives 101. Thus, 3333 is a member.
The divisors of 3333 are 1, 3, 11, 33, 101, 303, 1111, 3333. This sequence is approximately exponential.
MAPLE
n := 100; for a from 3 to n do if isprime(a) then for b from ceil((a-.5)^2) to floor((a+.5)^2) do if isprime(b) then c := (a^4+b^2)*(1/2); if isprime(c) then print(a*b*c) end if end if end do end if end do
PROG
(PARI) list(lim)=my(v=List(), t, a, c); forprime(b=2, , a=round(sqrt(b)); c=(a^4+b^2)/2; if(isprime(a) && denominator(c)==1 && isprime(c), t=a*b*c; if(t>lim, break); listput(v, a*b*c))); Set(v) \\ Charles R Greathouse IV, Aug 29 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
David Ferris, Aug 28 2015
STATUS
approved