This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
The first few terms are 1, 2, 2^2, 2*3, 2^3, 2^2*3, 2^4, 2^3*3, 2*3*5, ...
import Data.Set (singleton, fromList, deleteFindMin, union)
a025487 n = a025487_list !! (n-1)
a025487_list = 1 : h [b] (singleton b) bs where
(_ : b : bs) = a002110_list
h cs s xs'@(x:xs)
| m <= x = m : h (m:cs) (s' `union` fromList (map (* m) cs)) xs'
| otherwise = x : h (x:cs) (s `union` fromList (map (* x) (x:cs))) xs
where (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Apr 06 2013
isA025487 := proc(n) local pset,omega ; pset := sort(convert(numtheory[factorset](n),list)) ; omega := nops(pset) ; if op(-1,pset) <> ithprime(omega) then return false; end if; for i from 1 to omega-1 do if padic[ordp](n,ithprime(i)) < padic[ordp](n,ithprime(i+1)) then return false; end if; end do: true ; end proc: A025487 := proc(n) option remember ; local a; if n = 1 then 1 ; else for a from procname(n-1)+1 do if isA025487(a) then return a; end if; end do: end if; end proc: seq(A025487(n),n=1..100) ; # R. J. Mathar, May 25 2017
PrimeExponents[n_] := Last /@ FactorInteger[n]; lpe = {}; ln = {1}; Do[pe = Sort@PrimeExponents@n; If[ FreeQ[lpe, pe], AppendTo[lpe, pe]; AppendTo[ln, n]], {n, 2, 2350}]; ln (* Robert G. Wilson v, Aug 14 2004 *)
(* Second program: generate all terms m <= A002110(n): *)
f[n_] := {{1}}~Join~
Block[{lim = Product[Prime@ i, {i, n}],
ww = NestList[Append[#, 1] &, {1}, n - 1], dec},
dec[x_] := Apply[Times, MapIndexed[Prime[First@ #2]^#1 &, x]];
Map[Block[{w = #, k = 1},
Sort@ Prepend[If[Length@ # == 0, #, #[[1]]],
Product[Prime@ i, {i, Length@ w}] ] &@ Reap[
Do[
If[# < lim,
Sow[#]; k = 1,
If[k >= Length@ w, Break[], k++]] &@ dec@ Set[w,
If[k == 1,
MapAt[# + 1 &, w, k],
PadLeft[#, Length@ w, First@ #] &@
Drop[MapAt[# + Boole[i > 1] &, w, k], k - 1] ]],
{i, Infinity}] ][[-1]]
] &, ww]]; Sort[Join @@ f@ 13] (* Michael De Vlieger, May 19 2018 *)
isA025487(n)=my(k=valuation(n,2),t);n>>=k;forprime(p=3,default(primelimit),t=valuation(n,p);if(t>k,return(0),k=t);if(k,n/=p^k,return(n==1))) \\ Charles R Greathouse IV, Jun 10 2011
factfollow(n)={local(fm, np, n2);
fm=factor(n); np=matsize(fm)[1];
if(np==0,return([2]));
n2=n*nextprime(fm[np,1]+1);
if(np==1||fm[np,2]Franklin T. Adams-Watters, Dec 01 2011 */
is(n) = {if(n==1, return(1)); my(f = factor(n)); f[#f~, 1] == prime(#f~) && vecsort(f[, 2],,4) == f[, 2]} \\ David A. Corneth, Feb 14 2019
upto(Nmax)=vecsort(concat(vector(logint(Nmax,2),n,select(t->t<=Nmax,if(n>1,[factorback(primes(#p),Vecrev(p)) || p<-partitions(n)],[1,2]))))) \\ M. F. Hasler, Jul 17 2019
\\ For fast generation of large number of terms, use this program: A283980(n) = {my(f=factor(n)); prod(i=1, #f~, my(p=f[i, 1], e=f[i, 2]); if(p==2, 6, nextprime(p+1))^e)}; \\ From A283980 A025487list(e) = { my(lista = List([1, 2]), i=2, u = 2^e, t); while(lista[i] != u, if(2*lista[i] <= u, listput(lista,2*lista[i]); t = A283980(lista[i]); if(t <= u, listput(lista,t))); i++); vecsort(Vec(lista)); }; \\ Returns a list of terms up to the term 2^e. v025487 = A025487list(101); A025487(n) = v025487[n]; for(n=1,#v025487,print1(A025487(n), ", ")); \\ Antti Karttunen, Dec 24 2019
def sharp_primorial(n): return sloane.A002110(prime_pi(n)) N = 2310 nmax = 2^floor(log(N,2)) sorted([j for j in (prod(sharp_primorial(t[0])^t[1] for k, t in enumerate(factor(n))) for n in (1..nmax)) if j <= N]) # Giuseppe Coppoletta, Jan 26 2015
For example, 180 = 2^2 * 3^2 * 5^1 is present, because the maximal exponent in its prime factorization is 2, which occurs as an exponent of both 2 and 3, and because 180 is the minimal representative of the prime signature (2,2,1), as A046523(180) = 180.
A283980(n) = {my(f=factor(n)); prod(i=1, #f~, my(p=f[i, 1], e=f[i, 2]); if(p==2, 6, nextprime(p+1))^e)}; \\ From A283980 A025487list(e) = { my(lista = List([1, 2]), i=2, u = 2^e, t); while(lista[i] != u, if(2*lista[i] <= u, listput(lista,2*lista[i]); t = A283980(lista[i]); if(t <= u, listput(lista,t))); i++); vecsort(Vec(lista)); }; \\ Returns a list of terms up to the term 2^e. v025487 = A025487list(64); A025487(n) = v025487[n]; A330681(n) = A283980(A025487(n));
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