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 A357979 #10 Oct 04 2024 08:51:21
%S A357979 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,31,18,19,20,21,22,23,24,25,26,
%T A357979 27,28,29,30,59,32,33,62,35,36,37,38,39,40,127,42,79,44,45,46,47,48,
%U A357979 49,50,93,52,53,54,55,56,57,58,211,60,61,118,63,64,65,66
%N A357979 Second MTF-transform of A000041. Replace prime(k) with prime(A357977(k)) in the prime factorization of n.
%C A357979 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. We define the MTF-transform as applying a function horizontally along a number's prime indices; see the Mathematica program.
%e A357979 We have:
%e A357979 - 51 = prime(2) * prime(7),
%e A357979 - A357977(2) = 2,
%e A357979 - A357977(7) = 11,
%e A357979 - a(51) = prime(2) * prime(11) = 93.
%t A357979 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A357979 mtf[f_][n_]:=Product[If[f[i]==0,1,Prime[f[i]]],{i,primeMS[n]}];
%t A357979 Array[mtf[mtf[PartitionsP]],100]
%Y A357979 Other multiplicative sequences: A003961, A357852, A064988, A064989, A357980.
%Y A357979 Applying the transformation only once gives A357977, strict A357978.
%Y A357979 For primes instead of partition numbers we have A357983.
%Y A357979 A000040 lists the primes.
%Y A357979 A056239 adds up prime indices, row-sums of A112798.
%Y A357979 Cf. A000041, A000720, A003964, A063834, A076610, A215366, A296150, A299201, A299202, A357975.
%K A357979 nonn,mult
%O A357979 1,2
%A A357979 _Gus Wiseman_, Oct 24 2022