A357852 Replace prime(k) with prime(k+2) in the prime factorization of n.

1, 5, 7, 25, 11, 35, 13, 125, 49, 55, 17, 175, 19, 65, 77, 625, 23, 245, 29, 275, 91, 85, 31, 875, 121, 95, 343, 325, 37, 385, 41, 3125, 119, 115, 143, 1225, 43, 145, 133, 1375, 47, 455, 53, 425, 539, 155, 59, 4375, 169, 605, 161, 475, 61, 1715, 187, 1625, 203

Offset

1,2

Comments

This is the same as A045966 except the first term is 1 instead of 3.

Links

Table of n, a(n) for n=1..57.

Formula

a(n) = A003961(A003961(n)).

Example

The terms together with their prime indices begin:
    1: {}
    5: {3}
    7: {4}
   25: {3,3}
   11: {5}
   35: {3,4}
   13: {6}
  125: {3,3,3}
   49: {4,4}
   55: {3,5}
   17: {7}
  175: {3,3,4}
   19: {8}
   65: {3,6}
   77: {4,5}
  625: {3,3,3,3}

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Product[Prime[i+2], {i, primeMS[n]}], {n, 30}]

Prog

(PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k, 1] = nextprime(nextprime(f[k, 1]+1)+1)); factorback(f); \\ Michel Marcus, Oct 28 2022
(Python)
from math import prod
from sympy import nextprime, factorint
def A357852(n): return prod(nextprime(p, ith=2)**e for p, e in factorint(n).items()) # Chai Wah Wu, Oct 29 2022

Crossrefs

Applying the transformation only once gives A003961.

A permutation of A007310.

Other multiplicative sequences: A064988, A064989, A357977, A357980, A357983.

A000040 lists the primes.

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

Cf. A000720, A003964, A066207, A076610, A215366, A296150, A299201, A357979.

Sequence in context: A024864 A025108 A298900 * A166660 A354202 A037374

Adjacent sequences: A357849 A357850 A357851 * A357853 A357854 A357855

Keyword

nonn,mult

Author

Gus Wiseman, Oct 28 2022

Status

approved