OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..397 (calculated using the b-file at A033844)
FORMULA
If n = prime(e_1)...prime(e_k), then a(n) = prime(2^(e_1))...prime(2^(e_k)).
Sum_{n>=1} 1/a(n) = 1/Product_{k>=1} (1 - 1/prime(2^k)) = 1.90812936178871496289... . - Amiram Eldar, Dec 09 2022
EXAMPLE
The terms together with their prime indices begin:
1: {}
3: {2}
7: {4}
9: {2,2}
19: {8}
21: {2,4}
53: {16}
27: {2,2,2}
49: {4,4}
57: {2,8}
131: {32}
63: {2,2,4}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Times@@Prime/@(2^primeMS[n]), {n, 100}]
PROG
(PARI) a(n) = my(f=factor(n)); for(k=1, #f~, f[k, 1] = prime(2^primepi(f[k, 1]))); factorback(f); \\ Michel Marcus, May 20 2022
(Python)
from math import prod
from sympy import prime, primepi, factorint
def A353397(n): return prod(prime(2**primepi(p))**e for p, e in factorint(n).items()) # Chai Wah Wu, May 20 2022
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Gus Wiseman, May 17 2022
STATUS
approved