OFFSET
1,1
COMMENTS
Contains all the squared primes, plus additional terms.
At least some of these additional terms that are not divisible by 3 are given by the product of the smallest prime in a prime triplet, and the largest prime in that triplet, this certainly being true until the term 11413.
LINKS
Nathan Mabey, Table of n, a(n) for n = 1..20263
EXAMPLE
4 is a term since 4'' = 4, 4' = 4, and 2*4 - 4 - 4 = 0.
PROG
(Python)
from sympy import factorint
def d(n): return sum(n*e//p for p, e in factorint(n).items())
def ok(m): return m > 1 and 2*d(d(m)) - d(m) == 4
print([k for k in range(1, 999) if ok(k)]) # Michael S. Branicky, Aug 15 2022
(PARI) d(n) = if (n>0, my(f=factor(n)); sum(i=1, #f~, n*f[i, 2]/f[i, 1]), 0);
isok(m) = -2*d(d(m)) + d(m) + 4 == 0; \\ Michel Marcus, Apr 21 2020
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Nathan Mabey, Apr 20 2020
STATUS
approved