A370091 The smallest number such that exactly n numbers k exist such that a(n) - k = sopfr(a(n)) + sopfr(k), where sopfr(m) is the sum of the primes dividing m, with repetition.

6, 35, 77, 169, 287, 1147, 2623, 1517, 7739, 17792, 4352, 14647, 71107, 55488, 114091, 121673, 167137, 206837, 333797, 762079, 554484, 909157, 277928, 722473, 2165407, 3249569, 4328483, 2498227, 5271391, 5770603, 9178891, 8321771, 15732791, 16862017, 21067968, 9983680, 29496102

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..49

Formula

a(n) >= A369351(n).

Prog

(Python)
from sympy import factorint
from functools import cache
from itertools import count, islice
from collections import Counter
kcount, kmax = Counter(), 0
@cache
def sopfr(n): return sum(p*e for p, e in factorint(n).items())
def f(n):   # revised based on comment by David A. Corneth in A369351
    global kcount, kmax
    target = n - sopfr(n)
    for k in range(kmax+1, target+1):
        kcount[k+sopfr(k)] += 1
        kmax += 1
    return kcount[target]
def agen(): # generator of terms
    adict, n = dict(), 1
    for m in count(2):
        v = f(m)
        if v not in adict: adict[v] = m
        while n in adict: yield adict[n]; n += 1
print(list(islice(agen(), 12)))

Crossrefs

Cf. A001414, A369351.

Sequence in context: A198327 A009583 A369351 * A033578 A101077 A094952

Adjacent sequences: A370088 A370089 A370090 * A370092 A370093 A370094

Keyword

nonn

Author

Michael S. Branicky, Feb 09 2024

Extensions

More terms from David A. Corneth, Feb 11 2024

Status

approved