OFFSET
1,2
COMMENTS
The union is A308299.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..78 (calculated using the b-file at A062439)
FORMULA
Completely multiplicative with a(prime(n)) = prime(n!).
Sum_{n>=1} 1/a(n) = 1/Product_{k>=1} (1 - 1/prime(k!)) = 3.292606708493... . - Amiram Eldar, Dec 09 2022
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
3: {2}
4: {1,1}
13: {6}
6: {1,2}
89: {24}
8: {1,1,1}
9: {2,2}
26: {1,6}
659: {120}
12: {1,1,2}
5443: {720}
178: {1,24}
39: {2,6}
16: {1,1,1,1}
49033: {5040}
18: {1,2,2}
484037: {40320}
52: {1,1,6}.
MATHEMATICA
Table[Times@@Prime/@(If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]!), {n, 20}]
PROG
(PARI) A325709(n) = { my(f=factor(n)); prod(i=1, #f~, prime(primepi(f[i, 1])!)^f[i, 2]); }; \\ Antti Karttunen, Nov 17 2019
(Python)
from math import prod, factorial
from sympy import prime, primepi, factorint
def A325709(n): return prod(prime(factorial(primepi(p)))**e for p, e in factorint(n).items()) # Chai Wah Wu, Dec 26 2022
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Gus Wiseman, May 19 2019
EXTENSIONS
Keyword:mult added by Antti Karttunen, Nov 17 2019
STATUS
approved