A376294 The product of n's prime powers, with the base and exponent concatenated.
1, 21, 31, 22, 51, 651, 71, 23, 32, 1071, 111, 682, 131, 1491, 1581, 24, 171, 672, 191, 1122, 2201, 2331, 231, 713, 52, 2751, 33, 1562, 291, 33201, 311, 25, 3441, 3591, 3621, 704, 371, 4011, 4061, 1173, 411, 46221, 431, 2442, 1632, 4851, 471, 744, 72, 1092, 5301
Offset: 1
Examples
For n=5, a(5) = 51 since 5=5^1. For n=20, a(20) = 22*51 = 1122 since 20=2^2*5^1.
Links
- Haines Hoag, Table of n, a(n) for n = 1..10000
- Combo Class, The Mysterious Pattern I Found Within Prime Factorizations, Sep 12 2024.
Programs
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Maple
a:= n-> mul(parse(cat(i[])), i=ifactors(n)[2]): seq(a(n), n=1..51); # Alois P. Heinz, Sep 19 2024
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Mathematica
f[p_, e_] := 10^IntegerLength[e] * p + e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 26 2024 *)
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PARI
a(n)={my(f=factor(n)); prod(i=1, #f~, my([b,e]=f[i,]); b*10^(1+logint(e,10))+e)} \\ Andrew Howroyd, Sep 19 2024 -
Python
from math import prod from sympy import factorint def a(n): return prod(int(str(p)+str(e)) for p, e in factorint(n).items()) print([a(n) for n in range(1, 52)]) # Michael S. Branicky, Sep 27 2024
Formula
For primes p, a(p) = 10p + 1.
Comments