cp's OEIS Frontend

A380654 Number of positive integers less than or equal to n that have the same sum of distinct prime factors as n.

%I A380654 #11 Feb 16 2025 08:34:07
%S A380654 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,
%T A380654 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,
%U A380654 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
%N A380654 Number of positive integers less than or equal to n that have the same sum of distinct prime factors as n.
%C A380654 Ordinal transform of A008472.
%H A380654 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SumofPrimeFactors.html">Sum of Prime Factors</a>.
%F A380654 a(n) = |{j <= n : sopf(j) = sopf(n)}|.
%p A380654 b:= n-> add(i[1], i=ifactors(n)[2]):
%p A380654 p:= proc() 0 end:
%p A380654 a:= proc(n) option remember; local t;
%p A380654       t:= b(n); p(t):= p(t)+1
%p A380654     end:
%p A380654 seq(a(n), n=1..100);  # _Alois P. Heinz_, Jan 30 2025
%t A380654 sopf[n_] := DivisorSum[n, # &, PrimeQ[#] &]; Table[Length[Select[Range[n], sopf[#] == sopf[n] &]], {n, 1, 100}]
%o A380654 (Python)
%o A380654 from sympy import factorint
%o A380654 from collections import Counter
%o A380654 from itertools import count, islice
%o A380654 def agen(): # generator of terms
%o A380654     sopfcount = Counter()
%o A380654     for n in count(1):
%o A380654         key = sum(p for p in factorint(n))
%o A380654         sopfcount[key] += 1
%o A380654         yield sopfcount[key]
%o A380654 print(list(islice(agen(), 100))) # _Michael S. Branicky_, Jan 30 2025
%Y A380654 Cf. A008472, A067003, A263025, A380653.
%K A380654 nonn
%O A380654 1,4
%A A380654 _Ilya Gutkovskiy_, Jan 29 2025