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 A357978 #13 Oct 04 2024 08:51:25
%S A357978 1,2,2,4,3,4,3,8,4,6,5,8,7,6,6,16,11,8,13,12,6,10,19,16,9,14,8,12,29,
%T A357978 12,37,32,10,22,9,16,47,26,14,24,61,12,79,20,12,38,103,32,9,18,22,28,
%U A357978 131,16,15,24,26,58,163,24,199,74,12,64,21,20,251,44,38
%N A357978 Replace prime(k) with prime(A000009(k)) in the prime factorization of n.
%C A357978 In the definition, taking A000009(k) instead of prime(A000009(k)) gives A357982.
%e A357978 We have 90 = prime(1) * prime(2)^2 * prime(3), so a(90) = prime(1) * prime(1)^2 * prime(2) = 24.
%t A357978 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A357978 mtf[f_][n_]:=Product[If[f[i]==0,1,Prime[f[i]]],{i,primeMS[n]}];
%t A357978 Array[mtf[PartitionsQ],100]
%o A357978 (PARI) f9(n) = polcoeff( prod( k=1, n, 1 + x^k, 1 + x * O(x^n)), n); \\ A000009
%o A357978 a(n) = my(f=factor(n)); for (k=1, #f~, f[k,1] = prime(f9(primepi(f[k,1])))); factorback(f); \\ _Michel Marcus_, Oct 25 2022
%Y A357978 The non-strict version is A357977.
%Y A357978 Other multiplicative sequences: A003961, A357852, A064988, A064989, A357980.
%Y A357978 A000040 lists the primes.
%Y A357978 A056239 adds up prime indices, row-sums of A112798.
%Y A357978 Cf. A000041, A000720, A003964, A063834, A076610, A215366, A296150, A299201, A299202, A357975, A357979, A357983.
%K A357978 nonn,mult
%O A357978 1,2
%A A357978 _Gus Wiseman_, Oct 24 2022