A357977 Replace prime(k) with prime(A000041(k)) in the prime factorization of n.

1, 2, 3, 4, 5, 6, 11, 8, 9, 10, 17, 12, 31, 22, 15, 16, 47, 18, 79, 20, 33, 34, 113, 24, 25, 62, 27, 44, 181, 30, 263, 32, 51, 94, 55, 36, 389, 158, 93, 40, 547, 66, 761, 68, 45, 226, 1049, 48, 121, 50, 141, 124, 1453, 54, 85, 88, 237, 362, 1951, 60, 2659, 526

Offset

1,2

Comments

In the definition, taking A000041(k) instead of prime(A000041(k)) gives A299200.

Links

Table of n, a(n) for n=1..62.

Example

We have 35 = prime(3) * prime(4), so a(35) = prime(A000041(3)) * prime(A000041(4)) = prime(3) * prime(5) = 55.

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
mtf[f_][n_]:=Product[If[f[i]==0, 1, Prime[f[i]]], {i, primeMS[n]}];
Array[mtf[PartitionsP], 100]

Prog

(PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k, 1] = prime(numbpart(primepi(f[k, 1])))); factorback(f); \\ Michel Marcus, Oct 25 2022

Crossrefs

Applying the same transformation again gives A357979.

The strict version is A357978.

Other multiplicative sequences: A003961, A357852, A064988, A064989, A357980.

A000040 lists the primes.

A056239 adds up prime indices, row-sums of A112798.

Cf. A000041, A000720, A003964, A063834, A076610, A215366, A296150, A299201, A299202, A357975, A357983.

Sequence in context: A264968 A264967 A266641 * A222258 A266402 A266404

Adjacent sequences: A357974 A357975 A357976 * A357978 A357979 A357980

Keyword

nonn,mult

Author

Gus Wiseman, Oct 23 2022

Status

approved