OFFSET
1,1
COMMENTS
A048161 are primes p such that sigma_0((p*p+1)/2)= 2. Primes p such that sigma_0((p*p+1)/2)= 3 gives all RMS numbers (A140480) with 2 divisors (prime RMS numbers, prime NSW numbers (A088165)) and all RMS numbers with 4 divisors as those are a multiple of two nonequal RMS prime numbers. In general we look after primes p such that sigma_0((p*p+1)/2) equals some given integer k. RMS numbers n=p_1*...*p_t have k=2^t divisors (p_i prime, t integer >=1) and sigma_2(p_1*...*p_t)=(2^t)* (q_1^r_1 *...* q_t^r_t), q_j prime, r_t integer >=1.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
MAPLE
A066885 := proc(n) local p; p :=ithprime(n) ; (p^2+1)/2 ; end: A000005 := proc(n) numtheory[tau](n) ; end: for n from 2 to 300 do if A000005(A066885(n)) = 4 then printf("%d, ", ithprime(n)) ; fi; od: # R. J. Mathar, Sep 04 2008
MATHEMATICA
Select[Range[650], PrimeQ[#] && DivisorSigma[0, (#^2 + 1)/2] == 4 &] (* Amiram Eldar, Mar 11 2020 *)
Select[Prime[Range[150]], DivisorSigma[0, (#^2+1)/2]==4&] (* Harvey P. Dale, Sep 22 2022 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ctibor O. Zizka, Sep 02 2008
EXTENSIONS
97 inserted and extended by R. J. Mathar, Sep 04 2008
STATUS
approved