A322702 a(n) is the product of primes p such that p+1 divides n.

1, 1, 2, 3, 1, 10, 1, 21, 2, 1, 1, 330, 1, 13, 2, 21, 1, 170, 1, 57, 2, 1, 1, 53130, 1, 1, 2, 39, 1, 290, 1, 651, 2, 1, 1, 5610, 1, 37, 2, 399, 1, 5330, 1, 129, 2, 1, 1, 2497110, 1, 1, 2, 3, 1, 9010, 1, 273, 2, 1, 1, 10727970, 1, 61, 2, 651, 1, 10, 1, 201, 2

Offset

1,3

Comments

In general, a(n) is the product of A072627(n) distinct prime factors, with a(n) = 1 iff A072627(n) = 0.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10080

Formula

a(n) = Product_{p prime, p+1 divides n} p.

a(n) = denominator of Sum_{p prime, p+1 divides n} 1/p.

a(n) = Product_{d|n, d-1 is prime} (d-1), where d runs over the divisors of n.

a(2*n + 1) = 2, iff n == 1 (mod 3), else a(2*n + 1) = 1.

A001221(a(n)) = A072627(n). - Antti Karttunen, Jan 12 2019

Example

For n=12, the divisors of 12 are {1, 2, 3, 4, 6, 12}. The prime numbers p, such that p+1 is a divisor of 12, are {2, 3, 5, 11}, therefore a(12) = 2 * 3 * 5 * 11 = 330.

Maple

a:= n-> mul(`if`(isprime(d-1), d-1, 1), d=numtheory[divisors](n)):
seq(a(n), n=1..100);  # Alois P. Heinz, Dec 29 2018

Mathematica

Array[Apply[Times, Select[Divisors@ #, PrimeQ[# - 1] &] - 1 /. {} -> {1}] &, 69] (* Michael De Vlieger, Jan 07 2019 *)

Prog

(PARI) a(n) = my(d=divisors(n)); prod(k=1, #d, if(isprime(d[k]-1), d[k]-1, 1));

Crossrefs

Cf. A072627, A027760, A322356, A323156.

Sequence in context: A300838 A106342 A247563 * A107855 A211019 A298401

Adjacent sequences: A322699 A322700 A322701 * A322703 A322704 A322705

Keyword

nonn

Author

Daniel Suteu, Dec 23 2018

Status

approved