A280259 -id:A280259 - cp's OEIS frontend

A280258 a(n) = Sum_{d|n} pxi(d), where pxi(m) is the product of totatives of m (A001783).

1, 2, 3, 5, 25, 9, 721, 110, 2243, 215, 3628801, 397, 479001601, 20027, 896923, 2027135, 20922789888001, 87334, 6402373705728001, 8729939, 47297536723, 1253566127, 1124000727777607680001, 37182647, 41363226782215962649, 608621584727, 1524503639859202243

Offset: 1

Jaroslav Krizek, Jan 01 2017

nonn

Conjecture: a(n) is odd for numbers in A183300; a(n) is even for numbers in A001105 (2*n^2).

Numbers n such that a(n) is prime: 2, 3, 4, 9, 12, 20, 27, ... (there are no other terms < 742). Corresponding values of primes: 2, 3, 5, 2243, 397, 8729939, 1524503639859202243, ...

			For n=6; sets of totatives of divisors of 6: {1}, {1}, {1, 2}, {1, 5}; a(6) = 1+1+(1*2)+(1*5) = 9.

Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Cf. A001783, A001105, A183300, A280259, A280260.

[&+[&*[h: h in [1..d] | GCD(h,d) eq 1]: d in Divisors(n)]: n in [1..100]];

Table[Sum[Times @@ Select[Range@ d, CoprimeQ[#, d] &], {d, Divisors@ n}], {n, 27}] (* Michael De Vlieger, Jan 01 2017 *)

a(n) = sumdiv(n, d, prod(k=1, d, if (gcd(k,d)==1, k, 1))); \\ Michel Marcus, Jan 02 2017

a(n) = Sum_{d|n} A001783(d).

A280260 Partial products of A280258.

Original entry on oeis.org

1, 2, 6, 30, 750, 6750, 4866750, 535342500, 1200773227500, 258166243912500, 936833924075923912500, 371923067858141793262500, 178151744952881559857748513262500, 3567844996171358999271129475108087500, 3200082237501003827703259262202371164762500

Offset: 1

Jaroslav Krizek, Jan 01 2017

nonn

A280258(n) = Sum_{d|n} pxi(d), where pxi(m) is the product of totatives of m (A001783).

Cf. A001783, A280258, A280259.

[&*[&+[&*[h: h in [1..d] | GCD(h,d) eq 1]: d in Divisors(k)]: k in [1..n]]: n in [1..100]]

FoldList[#1 #2 &, #] &@ Table[Sum[Times @@ Select[Range@ d, CoprimeQ[#, d] &], {d, Divisors@ n}], {n, 15}] (* Michael De Vlieger, Jan 01 2017 *)

a(n) = Product_{i=1..n} A280258(i).

cp's OEIS Frontend

A280258 a(n) = Sum_{d|n} pxi(d), where pxi(m) is the product of totatives of m (A001783).

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