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

1,2

Comments

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

Links

Table of n, a(n) for n=1..60.

Eric Weisstein's World of Mathematics, Sum of Prime Factors

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A079445 A120173 A075862 * A022299 A099049 A217128

Adjacent sequences: A088682 A088683 A088684 * A088686 A088687 A088688

Keyword

nonn

Author

Eric W. Weisstein, Oct 05 2003

Status

approved