OFFSET
1,1
COMMENTS
Numbers m such that m*(m+1)/2 has exactly two divisors >= m.
Also numbers m such that m*(m+1)/2 is the product of two primes.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
FORMULA
EXAMPLE
10 is in the sequence, because there is only one nontrivial decomposition of {1..10} into subsets with equal element sum: {1,10}, {2,9}, {3,8}, {4,7}, {5,6}; 11|55.
13 is in the sequence with decomposition of {1..13}: {1,12}, {2,11}, {3,10}, {4,9}, {5,8}, {6,7}, {13}; 13|91.
MAPLE
a:= proc(n) option remember; local k;
for k from 1+ `if`(n=1, 2, a(n-1))
while not (isprime(k) and isprime((k+1)/2)
or isprime(k+1) and isprime(k/2))
do od; k
end:
seq(a(n), n=1..100);
MATHEMATICA
Select[Range@1304, PrimeOmega[#] + PrimeOmega[# + 1] == 3 &] (* Robert G. Wilson v, Jun 28 2010 and updated Sep 21 2018 *)
PROG
(PARI) is(n)=if(isprime(n), bigomega(n+1)==2, isprime(n+1) && bigomega(n)==2) \\ Charles R Greathouse IV, Sep 08 2015
(PARI) is(n)=if(n%2, isprime((n+1)/2) && isprime(n), isprime(n/2) && isprime(n+1)) \\ Charles R Greathouse IV, Mar 16 2022
(PARI) list(lim)=my(v=List()); forprime(p=3, lim, if(isprime((p+1)/2), listput(v, p))); forprime(p=5, lim+1, if(isprime(p\2), listput(v, p-1))); Set(v) \\ Charles R Greathouse IV, Mar 16 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Sep 03 2009
STATUS
approved