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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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+=[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

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Last modified February 28 11:45 EST 2021. Contains 341703 sequences. (Running on oeis4.)