A349164 a(n) = A064989(A003961(n) / 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, 1, 3, 4, 5, 3, 7, 4, 9, 5, 11, 12, 13, 7, 15, 16, 17, 9, 19, 2, 21, 11, 23, 4, 25, 13, 9, 28, 29, 15, 31, 8, 33, 17, 35, 36, 37, 19, 39, 10, 41, 21, 43, 22, 45, 23, 47, 48, 49, 25, 51, 52, 53, 9, 55, 28, 19, 29, 59, 6, 61, 31, 63, 64, 13, 33, 67, 17, 69, 35, 71, 12, 73, 37, 75, 76, 77, 39, 79, 40, 81, 41, 83, 84

Offset

1,3

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(A349161(n)).

a(n) = n / A349163(n).

Mathematica

Array[Times @@ Map[If[#1 <= 2, 1, NextPrime[#1, -1]]^#2 & @@ # &, FactorInteger[#2/GCD[##]]] & @@ {DivisorSigma[1, #], Times @@ Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]]} &, 84] (* 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); };
A349164(n) = { my(u=A003961(n)); A064989(u/gcd(u, sigma(n))); };

Crossrefs

Cf. A000203, A003961, A319630, A326042, A336702, A342671, A348993, A349161, A349162, A349169, A349174.

Cf. A349144 and A349168 [positions where a(n) is / is not relatively prime with A349163(n) = n/a(n)].

Sequence in context: A350640 A354932 A123901 * A214682 A093395 A176774

Adjacent sequences: A349161 A349162 A349163 * A349165 A349166 A349167

Keyword

nonn

Author

Antti Karttunen, Nov 09 2021

Status

approved