OFFSET
1,1
COMMENTS
If p, (3/2)*(p+1), (3/2)*(p^2+p)+1 and (3/2)*(p^2+1)+2*p are all prime, then (3/2)*p*(3*p^2+4*p+3) is a term. The Generalized Bunyakovsky Conjecture implies that there are infinitely many of these. - Robert Israel, Apr 15 2022
LINKS
Robert Israel, Table of n, a(n) for n = 1..2500
MATHEMATICA
SequencePosition[Table[n+Total[Times@@@FactorInteger[n]], {n, 58000}], {x_, x_}][[;; , 1]] (* Harvey P. Dale, Feb 26 2023 *)
PROG
(PARI) A075254(n) = my(f = factor(n)); n + sum(i=1, #f~, f[i, 1]*f[i, 2]);
(Python)
from sympy import factorint
from itertools import count, islice
def sopf(n): return sum(p*e for p, e in factorint(n).items())
def agen(): # generator of terms
sopfkplus1 = 2
for k in count(2):
sopfk, sopfkplus1 = sopfkplus1, sopf(k+1)
if k + sopfk == k + 1 + sopfkplus1: yield k
print(list(islice(agen(), 42))) # Michael S. Branicky, Apr 15 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
EXTENSIONS
More terms from Michel Marcus, Jun 05 2014
STATUS
approved