cp's OEIS Frontend

A380653 Number of positive integers less than or equal to n that have the same sum of prime factors (with repetition) as n.

%I A380653 #12 Feb 16 2025 08:34:07
%S A380653 1,1,1,1,1,2,1,1,2,2,1,3,1,1,1,2,1,3,1,2,1,2,1,3,2,1,4,2,1,3,1,4,1,2,
%T A380653 1,5,1,1,1,3,1,2,1,2,4,1,1,5,2,3,1,2,1,6,2,3,1,2,1,4,1,1,4,5,1,3,1,2,
%U A380653 1,3,1,6,1,1,5,2,2,3,1,6,7,2,1,4,2,1,1,3,1,7,2,1,1,1,1,8,1,4,4,5
%N A380653 Number of positive integers less than or equal to n that have the same sum of prime factors (with repetition) as n.
%C A380653 Ordinal transform of A001414.
%H A380653 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SumofPrimeFactors.html">Sum of Prime Factors</a>.
%F A380653 a(n) = |{j <= n : sopfr(j) = sopfr(n)}|.
%p A380653 b:= n-> add(i[1]*i[2], i=ifactors(n)[2]):
%p A380653 p:= proc() 0 end:
%p A380653 a:= proc(n) option remember; local t;
%p A380653       t:= b(n); p(t):= p(t)+1
%p A380653     end:
%p A380653 seq(a(n), n=1..100);  # _Alois P. Heinz_, Jan 30 2025
%t A380653 sopfr[1] = 0; sopfr[n_] := Plus @@ Times @@@ FactorInteger@ n; Table[Length[Select[Range[n], sopfr[#] == sopfr[n] &]], {n, 1, 100}]
%o A380653 (Python)
%o A380653 from sympy import factorint
%o A380653 from collections import Counter
%o A380653 from itertools import count, islice
%o A380653 def agen(): # generator of terms
%o A380653     sopfrcount = Counter()
%o A380653     for n in count(1):
%o A380653         key = sum(p*e for p, e in factorint(n).items())
%o A380653         sopfrcount[key] += 1
%o A380653         yield sopfrcount[key]
%o A380653 print(list(islice(agen(), 100))) # _Michael S. Branicky_, Jan 30 2025
%Y A380653 Cf. A001414, A058933, A263025, A380654.
%K A380653 nonn
%O A380653 1,6
%A A380653 _Ilya Gutkovskiy_, Jan 29 2025