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A088686 Positions of the records in the sum-of-primes function sopfr(n) if sopfr(prime) is taken to be 0.

%I A088686 #23 Feb 16 2025 08:32:51
%S A088686 1,4,6,8,10,14,21,22,26,34,38,46,58,62,74,82,86,94,106,118,122,134,
%T A088686 142,146,158,166,178,194,202,206,214,218,226,254,262,274,278,298,302,
%U A088686 314,326,334,346,358,362,382,386,394,398,422,446,454,458,466,478,482
%N A088686 Positions of the records in the sum-of-primes function sopfr(n) if sopfr(prime) is taken to be 0.
%H A088686 Indranil Ghosh, <a href="/A088686/b088686.txt">Table of n, a(n) for n = 1..2765</a> (terms < 50000)
%H A088686 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SumofPrimeFactors.html">Sum of Prime Factors</a>
%t A088686 Function[s, Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]] ]@ Table[Total@ Flatten@ Map[ConstantArray[#1, #2] /. 1 -> 0 & @@ # &, FactorInteger@ n] - n Boole[PrimeQ@ n], {n, 500}] (* _Michael De Vlieger_, Jun 29 2017 *)
%o A088686 (PARI) sopfr(k) = my(f=factor(k)); sum(j=1, #f~, f[j, 1]*f[j, 2]);
%o A088686 lista(nn) = {my(record = -1); for (n=1, nn, if (! isprime(n), if ((x=sopfr(n)) > record, record = x; print1(n, ", "));););} \\ _Michel Marcus_, Jun 29 2017
%o A088686 (Python)
%o A088686 from sympy import factorint, isprime
%o A088686 def sopfr(n):
%o A088686     f=factorint(n)
%o A088686     return sum([i*f[i] for i in f])
%o A088686 l=[]
%o A088686 record=-1
%o A088686 for n in range(1, 501):
%o A088686     if not isprime(n):
%o A088686         x=sopfr(n)
%o A088686         if x>record:
%o A088686             record=x
%o A088686             l.append(n)
%o A088686 print(l) # _Indranil Ghosh_, Jun 29 2017
%Y A088686 Cf. A001414, A088685.
%K A088686 nonn
%O A088686 1,2
%A A088686 _Eric W. Weisstein_, Oct 05 2003