A325709 Replace k with k! in the prime indices of n.
1, 2, 3, 4, 13, 6, 89, 8, 9, 26, 659, 12, 5443, 178, 39, 16, 49033, 18, 484037, 52, 267, 1318, 5222429, 24, 169, 10886, 27, 356, 61194647, 78, 774825383, 32, 1977, 98066, 1157, 36, 10552185239, 968074, 16329, 104, 153903050137, 534, 2394322471421, 2636, 117
Offset: 1
Examples
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}.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..78 (calculated using the b-file at A062439)
- Index entries for sequences computed from indices in prime factorization.
Crossrefs
Programs
-
Mathematica
Table[Times@@Prime/@(If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]!),{n,20}] -
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
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
Extensions
Keyword:mult added by Antti Karttunen, Nov 17 2019
Comments