%I #57 Jan 09 2024 16:56:27
%S 4,9,21,25,33,49,57,69,85,93,121,129,133,145,169,177,205,213,217,237,
%T 249,253,265,289,309,361,393,417,445,469,489,493,505,517,529,553,565,
%U 573,597,633,669,685,697,753,781,793,813,817,841,865,889,913,933,949,961,973,985,993
%N Numbers m that are solutions of the arithmetic differential equation 2m" - m' - 4 = 0.
%C Contains all the squared primes, plus additional terms.
%C 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.
%H Nathan Mabey, <a href="/A334261/b334261.txt">Table of n, a(n) for n = 1..20263</a>
%e 4 is a term since 4'' = 4, 4' = 4, and 2*4 - 4 - 4 = 0.
%o (Python)
%o from sympy import factorint
%o def d(n): return sum(n*e//p for p, e in factorint(n).items())
%o def ok(m): return m > 1 and 2*d(d(m)) - d(m) == 4
%o print([k for k in range(1, 999) if ok(k)]) # _Michael S. Branicky_, Aug 15 2022
%o (PARI) d(n) = if (n>0, my(f=factor(n)); sum(i=1, #f~, n*f[i, 2]/f[i, 1]), 0);
%o isok(m) = -2*d(d(m)) + d(m) + 4 == 0; \\ _Michel Marcus_, Apr 21 2020
%Y Cf. A003415 (n'), A068346 (n"), A001248 (squared primes), A368701 (characteristic function).
%Y Cf. also A189941.
%K easy,nonn
%O 1,1
%A _Nathan Mabey_, Apr 20 2020