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

1,2

Links

Indranil Ghosh, Table of n, a(n) for n = 1..2765 (terms < 50000)

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

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 *)

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(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

Crossrefs

Cf. A001414, A088685.

Sequence in context: A327888 A103800 A022449 * A161344 A127792 A288814

Adjacent sequences: A088683 A088684 A088685 * A088687 A088688 A088689

Keyword

nonn

Author

Eric W. Weisstein, Oct 05 2003

Status

approved