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A088685 Records for the sum-of-primes function sopfr(n) if sopfr(prime) is taken to be 0.

%I A088685 #30 Apr 22 2025 14:07:53
%S A088685 0,4,5,6,7,9,10,13,15,19,21,25,31,33,39,43,45,49,55,61,63,69,73,75,81,
%T A088685 85,91,99,103,105,109,111,115,129,133,139,141,151,153,159,165,169,175,
%U A088685 181,183,193,195,199,201,213,225,229,231,235,241,243,253,259,265,271
%N A088685 Records for the sum-of-primes function sopfr(n) if sopfr(prime) is taken to be 0.
%C A088685 A048974, A052147 and A067187 are very similar after dropping terms less than 13. - _Eric W. Weisstein_, Oct 10 2003
%H A088685 Robert Price, <a href="/A088685/b088685.txt">Table of n, a(n) for n = 1..10000</a>
%H A088685 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SumofPrimeFactors.html">Sum of Prime Factors</a>
%t A088685 Union@ FoldList[Max, Table[Total@ Flatten@ Map[ConstantArray[#1, #2] /. 1 -> 0 & @@ # &, FactorInteger@ n] - n Boole[PrimeQ@ n], {n, 540}]] (* _Michael De Vlieger_, Jun 29 2017 *)
%o A088685 (PARI) sopfr(k) = my(f=factor(k)); sum(j=1, #f~, f[j, 1]*f[j, 2]);
%o A088685 lista(nn) = {my(record = -1); for (n=1, nn, if (! isprime(n), if ((x=sopfr(n)) > record, record = x; print1(record, ", "));););} \\ _Michel Marcus_, Jun 29 2017
%o A088685 (Python)
%o A088685 from sympy import factorint, isprime
%o A088685 def sopfr(n):
%o A088685     f=factorint(n)
%o A088685     return sum([i*f[i] for i in f])
%o A088685 l=[]
%o A088685 record=-1
%o A088685 for n in range(1, 501):
%o A088685     if not isprime(n):
%o A088685         x=sopfr(n)
%o A088685         if x>record:
%o A088685             record=x
%o A088685             l.append(record)
%o A088685 print(l) # _Indranil Ghosh_, Jun 29 2017
%Y A088685 Cf. A001414, A048974, A052147, A067187, A088686.
%K A088685 nonn
%O A088685 1,2
%A A088685 _Eric W. Weisstein_, Oct 05 2003