A380654 Number of positive integers less than or equal to n that have the same sum of distinct prime factors as n.
1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 1, 1, 4, 1, 4, 1, 3, 1, 2, 1, 5, 6, 1, 3, 2, 1, 2, 1, 5, 1, 2, 1, 7, 1, 1, 1, 4, 1, 2, 1, 3, 2, 1, 1, 8, 5, 6, 1, 2, 1, 9, 2, 3, 1, 2, 1, 3, 1, 1, 4, 6, 1, 3, 1, 3, 1, 2, 1, 10, 1, 1, 3, 2, 2, 3, 1, 7, 4, 2, 1, 3, 2, 1, 1, 4, 1, 5, 2, 2, 1, 1, 1, 11, 1, 4, 3, 8
Offset: 1
Keywords
Links
- Eric Weisstein's World of Mathematics, Sum of Prime Factors.
Programs
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Maple
b:= n-> add(i[1], i=ifactors(n)[2]): p:= proc() 0 end: a:= proc(n) option remember; local t; t:= b(n); p(t):= p(t)+1 end: seq(a(n), n=1..100); # Alois P. Heinz, Jan 30 2025 -
Mathematica
sopf[n_] := DivisorSum[n, # &, PrimeQ[#] &]; Table[Length[Select[Range[n], sopf[#] == sopf[n] &]], {n, 1, 100}] -
Python
from sympy import factorint from collections import Counter from itertools import count, islice def agen(): # generator of terms sopfcount = Counter() for n in count(1): key = sum(p for p in factorint(n)) sopfcount[key] += 1 yield sopfcount[key] print(list(islice(agen(), 100))) # Michael S. Branicky, Jan 30 2025
Formula
a(n) = |{j <= n : sopf(j) = sopf(n)}|.
Comments