A370356 a(n) is the smallest number such that exactly n numbers k exist with k - a(n) = sopfr(k) + sopfr(a(n)), where sopfr(m) is the sum of the primes dividing m with repetition.

4, 1, 6, 22, 46, 526, 1509, 838, 6238, 5667, 20158, 32127, 56697, 82617, 177598, 174718, 384382, 314492, 415789, 498957, 1142398, 1884958, 1713598, 2620798, 2280067, 5209342, 4324316, 5847653, 7796863, 16516489, 6918908, 9979197, 15855829, 24023995, 31600797

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..43

Michael S. Branicky, Terms a(n) <= 10^8 (else -1)

Formula

a(n) >= A370352(n).

Prog

(Python)
from sympy import factorint
from itertools import count, islice
from collections import Counter
kcount, kmax = Counter(), 0
def sopfr(n): return sum(p*e for p, e in factorint(n).items())
def f(n):
    global kcount, kmax
    target = n + sopfr(n)
    for k in range(kmax+1, 2*target+5):
        kcount[k-sopfr(k)] += 1
        kmax += 1
    return kcount[target]
def agen(): # generator of terms
    adict, n = dict(), 1
    for m in count(1):
        v = f(m)
        if v not in adict: adict[v] = m
        while n in adict: yield adict[n]; n += 1
print(list(islice(agen(), 16)))

Crossrefs

Cf. A001414, A370352, A370091.

Sequence in context: A140895 A343599 A191714 * A126150 A364509 A349545

Adjacent sequences: A370352 A370353 A370355 * A370357 A370358 A370359

Keyword

nonn

Author

Michael S. Branicky, Feb 16 2024

Status

approved