%I #30 Jan 12 2021 19:10:46
%S 2,3,8,5,11,7,26,15,17,11,43,13,23,23,80,17,47,19,89,31,35,23,171,35,
%T 41,63,151,29,95,31,242,47,53,47,175,37,59,55,521,41,159,43,323,131,
%U 71,47,683,63,107,71,433,53,191,71,1175,79,89,59,527,61,95,223,728
%N Treat the prime factors of n in ascending order as digits of a number in base "greatest prime factor + 1" and convert this number back to a decimal number.
%H Alois P. Heinz, <a href="/A340393/b340393.txt">Table of n, a(n) for n = 2..20000</a>
%F a(p) = p for prime p.
%e Some examples for the calculation of a(n):
%e (For digits 10,11...36 the letters A,B...Z are used.)
%e n -> prime factors -> a(n)(base) -> a(n)(base 10)
%e 6 -> 2 * 3 -> 23 (4) -> 11
%e 20 -> 2 * 2 * 5 -> 225 (6) -> 89
%e 33 -> 3 * 11 -> 3B (12) -> 47
%e 56 -> 2 * 2 * 2 * 7 -> 2227 (8) -> 1175
%e 62 -> 2 * 31 -> 2U (32) -> 95
%e 72 -> 2 * 2 * 2 * 3 * 3 ->22233 (4) -> 687
%e 100 -> 2 * 2 * 5 * 5 -> 2255 (6) -> 539
%e 910 -> 2 * 5 * 7 * 13 -> 257D (14) -> 6579
%p a:= n-> (l-> (m-> add(l[-i]*m^(i-1), i=1..nops(l)))(1+
%p max(l)))(map(i-> i[1]$i[2], sort(ifactors(n)[2]))):
%p seq(a(n), n=2..77); # _Alois P. Heinz_, Jan 09 2021
%o (Python)
%o def A(startn,lastn=0):
%o a,n,lastn=[],startn,max(lastn,startn)
%o while n<=lastn:
%o i,j,v,m,f=2,0,0,n,[]
%o while i<m**(0.5)+0.1:
%o if m//i==m/i:
%o f.append(i)
%o m,i=m//i,1
%o i+=1
%o f.append(m)
%o while j<len(f):v,j=v+f[j]*((f[len(f)-1]+1)**(len(f)-j-1)),j+1
%o print(str(n)+" "+str(v))
%o a.append([v])
%o n+=1
%o return a
%o (Python)
%o from sympy import factorint
%o def fromdigits(d, b):
%o n = 0
%o for di in d: n *= b; n += di
%o return n
%o def a(n):
%o f = sorted(factorint(n, multiple=True))
%o return fromdigits(f, f[-1]+1)
%o print([a(n) for n in range(2, 76)]) # _Michael S. Branicky_, Jan 06 2021
%o (PARI) a(n) = my(f=factor(n), list=List()); for (k=1, #f~, for (j=1, f[k, 2], listput(list, f[k,1]))); fromdigits(Vec(list), vecmax(f[,1])+1); \\ _Michel Marcus_, Jan 06 2021
%Y Cf. A037274 (home primes), A037276, A340394.
%K nonn,look,base
%O 2,1
%A _S. Brunner_, Jan 06 2021