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A322702 a(n) is the product of primes p such that p+1 divides n. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 27 15:59 EST 2020. Contains 332307 sequences. (Running on oeis4.)