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

1, 4, 6, 8, 10, 14, 21, 22, 26, 34, 38, 46, 58, 62, 74, 82, 86, 94, 106, 118, 122, 134, 142, 146, 158, 166, 178, 194, 202, 206, 214, 218, 226, 254, 262, 274, 278, 298, 302, 314, 326, 334, 346, 358, 362, 382, 386, 394, 398, 422, 446, 454, 458, 466, 478, 482

Offset: 1

Author

Eric W. Weisstein, Oct 05 2003

Keywords

• nonn

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..2765 (terms < 50000)
• Eric Weisstein's World of Mathematics, Sum of Prime Factors

Crossrefs

Cf. A001414, A088685.

Programs

Mathematica

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 *)

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(n, ", "));););} \\ 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(n)
print(l) # Indranil Ghosh, Jun 29 2017