This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A384915 #7 Jun 12 2025 10:24:48
%S A384915 1,1,1,2,1,1,1,2,2,1,1,2,1,1,1,3,1,2,1,2,1,1,1,2,2,1,3,2,1,1,1,3,1,1,
%T A384915 1,4,1,1,1,2,1,1,1,2,2,1,1,3,2,2,1,2,1,3,1,2,1,1,1,2,1,1,2,4,1,1,1,2,
%U A384915 1,1,1,4,1,1,2,2,1,1,1,3,4,1,1,2,1,1,1
%N A384915 The number of unordered factorizations of n into powers of primes of the form p^e where p is prime and 0 <= e <= p (A074583).
%H A384915 Amiram Eldar, <a href="/A384915/b384915.txt">Table of n, a(n) for n = 1..10000</a>
%F A384915 Multiplicative with a(p^e) = A026820(e, p).
%F A384915 a(n) >= A384916(n), with equality if and only if n is in A048103.
%e A384915 a(4) = 2 since 4 has 2 factorizations: 2^1 * 2^1 and 2^2, with exponents 1 and 2 that are <= 2.
%t A384915 f[p_, e_] := Length[IntegerPartitions[e, p]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A384915 (PARI) T(n, k)=my(s); forpart(v=n, s++, , k); s \\ _Charles R Greathouse IV_ at A026820
%o A384915 a(n) = {my(f = factor(n)); prod(i = 1, #f~, T(f[i,2], f[i,1]));}
%Y A384915 Cf. A026820, A048103, A074583.
%Y A384915 Similar sequences: A000688, A046951, A050361, A050377, A188581, A188585, A322885, A370256, A384912, A384913, A384914, A384916.
%K A384915 nonn,easy,mult
%O A384915 1,4
%A A384915 _Amiram Eldar_, Jun 12 2025