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

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, 85, 91, 99, 103, 105, 109, 111, 115, 129, 133, 139, 141, 151, 153, 159, 165, 169, 175, 181, 183, 193, 195, 199, 201, 213, 225, 229, 231, 235, 241, 243, 253, 259, 265, 271

Offset: 1

Author

Eric W. Weisstein, Oct 05 2003

Keywords

• nonn

Comments

A048974, A052147 and A067187 are very similar after dropping terms less than 13. - Eric W. Weisstein, Oct 10 2003

Links

• Robert Price, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Sum of Prime Factors

Crossrefs

Cf. A001414, A048974, A052147, A067187, A088686.

Programs

Mathematica

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 *)

PARI

sopfr(k) = my(f=factor(k)); sum(j=1, #f~, f[j, 1]*f[j, 2]);
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

Python

from sympy import factorint, isprime
def sopfr(n):
    f=factorint(n)
    return sum([i*f[i] for i in f])
l=[]
record=-1
for n in range(1, 501):
    if not isprime(n):
        x=sopfr(n)
        if x>record:
            record=x
            l.append(record)
print(l) # Indranil Ghosh, Jun 29 2017