

A249140


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


2



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
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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): (21)*(21)=1.
a(4)=4 because the 4th composite number is 9, and the prime factors of 9 are (3,3): (31)*(31)=4.
a(19)=8 because the 19th composite number is 30, and the prime factors of 30 are (2,3,5): (21)*(31)*(51)=8.


MAPLE

b:= proc(n) option remember; local k;
for k from 1+`if`(n=1, 3, b(n1))
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; (p1)^e, {pe, FactorInteger[n]}];
b /@ Select[Range[100], CompositeQ] (* JeanFrançois Alcover, Nov 13 2020 *)


PROG

(PARI) b(n) = my(f=factor(n)); f[, 1] = apply(x>(x1), 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



