A349163 a(n) = A064989(gcd(sigma(n), A003961(n))), where A003961 shifts the prime factorization of n one step towards larger primes, while A064989 shifts it back towards smaller primes, and sigma is the sum of divisors function.

1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 10, 1, 2, 1, 6, 1, 2, 3, 1, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 6, 1, 2, 3, 2, 1, 10, 1, 2, 1, 1, 5, 2, 1, 4, 1, 2, 1, 6, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 3, 4, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 11, 5, 1, 2, 1, 2, 1

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..22968

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = A064989(A342671(n)).

a(n) = n / A349164(n).

Mathematica

Array[Times @@ Map[If[#1 <= 2, 1, NextPrime[#1, -1]]^#2 & @@ # &, FactorInteger@ GCD[##]] & @@ {DivisorSigma[1, #], Times @@ Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]]} &, 105] (* Michael De Vlieger, Nov 11 2021 *)

Prog

(PARI)
A003961(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A064989(n) = { my(f=factor(n)); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for(i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };
A349163(n) = A064989(gcd(sigma(n), A003961(n)));

Crossrefs

Cf. A000203, A003961, A342671, A349161, A349162, A349165 (positions of 1's), A349166 (of terms > 1).

Cf. A349144 and A349168 [positions where a(n) is / is not relatively prime with A349164(n) = n/a(n)].

Sequence in context: A045887 A056832 A105931 * A279495 A300409 A361631

Adjacent sequences: A349160 A349161 A349162 * A349164 A349165 A349166

Keyword

nonn

Author

Antti Karttunen, Nov 09 2021

Status

approved