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

1,2

Links

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

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A002808, A003958, A114434.

Sequence in context: A086145 A309086 A261070 * A113421 A135366 A247248

Adjacent sequences: A249137 A249138 A249139 * A249141 A249142 A249143

Keyword

nonn,easy

Author

Gil Broussard, Oct 22 2014

Status

approved