cp's OEIS Frontend

A376294 The product of n's prime powers, with the base and exponent concatenated.

%I A376294 #37 Oct 24 2024 14:46:45
%S A376294 1,21,31,22,51,651,71,23,32,1071,111,682,131,1491,1581,24,171,672,191,
%T A376294 1122,2201,2331,231,713,52,2751,33,1562,291,33201,311,25,3441,3591,
%U A376294 3621,704,371,4011,4061,1173,411,46221,431,2442,1632,4851,471,744,72,1092,5301
%N A376294 The product of n's prime powers, with the base and exponent concatenated.
%C A376294 Multiplicative with a(p^e) = the concatenation of p and e.
%C A376294 A prime which occurs just once in the factorization of n is taken as exponent 1 so that for instance n = 7 = 7^1 becomes 71.
%C A376294 It is unknown whether there are any fixed points a(n) = n beyond n=1.
%H A376294 Haines Hoag, <a href="/A376294/b376294.txt">Table of n, a(n) for n = 1..10000</a>
%H A376294 Combo Class, <a href="https://www.youtube.com/watch?v=pylw9t4j6bM">The Mysterious Pattern I Found Within Prime Factorizations</a>, Sep 12 2024.
%F A376294 For primes p, a(p) = 10p + 1.
%e A376294 For n=5, a(5) = 51 since 5=5^1.
%e A376294 For n=20, a(20) = 22*51 = 1122 since 20=2^2*5^1.
%p A376294 a:= n-> mul(parse(cat(i[])), i=ifactors(n)[2]):
%p A376294 seq(a(n), n=1..51);  # _Alois P. Heinz_, Sep 19 2024
%t A376294 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 *)
%o A376294 (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
%o A376294 (Python)
%o A376294 from math import prod
%o A376294 from sympy import factorint
%o A376294 def a(n): return prod(int(str(p)+str(e)) for p, e in factorint(n).items())
%o A376294 print([a(n) for n in range(1, 52)]) # _Michael S. Branicky_, Sep 27 2024
%Y A376294 Cf. A376254 (indices of a(n) < n), A287483 (indices of local maxima).
%K A376294 nonn,base,mult
%O A376294 1,2
%A A376294 _Haines Hoag_, Sep 19 2024