A249140 To obtain a(n), write the n-th composite number as a product of primes, subtract 1 from each prime and multiply.

1, 2, 1, 4, 4, 2, 6, 8, 1, 4, 4, 12, 10, 2, 16, 12, 8, 6, 8, 1, 20, 16, 24, 4, 18, 24, 4, 12, 10, 16, 22, 2, 36, 16, 32, 12, 8, 40, 6, 36, 28, 8, 30, 24, 1, 48, 20, 16, 44, 24, 4, 36, 32, 18, 60, 24, 4, 16, 40, 12, 64, 42, 56, 10, 16, 72, 22, 60, 46, 72, 2

Offset: 1

Author

Gil Broussard, Oct 22 2014

Keywords

• nonn
• easy

Examples

			a(1)=1 because the 1st composite number is 4, and the prime factors of 4 are (2,2): (2-1)*(2-1)=1.
a(4)=4 because the 4th composite number is 9, and the prime factors of 9 are (3,3): (3-1)*(3-1)=4.
a(19)=8 because the 19th composite number is 30, and the prime factors of 30 are (2,3,5): (2-1)*(3-1)*(5-1)=8.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002808, A003958, A114434.

Programs

Maple

b:= proc(n) option remember; local k;
      for k from 1+`if`(n=1, 3, b(n-1))
      while isprime(k) do od; k
    end:
a:= n-> mul((i[1]-1)^i[2], i=ifactors(b(n))[2]):
seq(a(n), n=1..100);  # Alois P. Heinz, Oct 23 2014

Mathematica

b[n_] := Product[{p, e} = pe; (p-1)^e, {pe, FactorInteger[n]}];
b /@ Select[Range[100], CompositeQ] (* Jean-François Alcover, Nov 13 2020 *)

PARI

b(n) = my(f=factor(n)); f[,1] = apply(x->(x-1), f[,1]); factorback(f); \\ A003958
lista(nn) = apply(b, select(x->((x != 1) && !isprime(x)), [1..nn])); \\ Michel Marcus, Nov 13 2020

Formula

a(n) = A003958(A002808(n)). - Michel Marcus, Oct 22 2014