A348993 - OEIS

A348993

a(n) = A064989(sigma(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, 1, 5, 2, 1, 1, 3, 11, 2, 2, 5, 5, 1, 2, 29, 4, 11, 3, 1, 1, 2, 2, 1, 29, 5, 1, 5, 6, 2, 1, 5, 2, 4, 2, 55, 17, 3, 5, 3, 10, 1, 7, 5, 22, 2, 2, 29, 34, 29, 4, 25, 8, 1, 4, 3, 1, 6, 6, 1, 29, 1, 11, 113, 2, 2, 13, 5, 2, 2, 4, 11, 31, 17, 29, 15, 2, 5, 3, 29, 49, 10, 10, 5, 8, 7, 2, 3, 12, 22, 5, 5, 1, 2, 6, 5

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

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(A349162(n)) = A064989(A348992(n)).

MATHEMATICA

Array[Times @@ Map[If[#1 <= 2, 1, NextPrime[#1, -1]]^#2 & @@ # &, FactorInteger[#1/GCD[##]]] & @@ {DivisorSigma[1, #], Times @@ Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]]} &, 96] (* 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); 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)};

A349162(n) = { my(s=sigma(n)); (s/gcd(s, A003961(n))); };

A348993(n) = A064989(A349162(n));

CROSSREFS

Cf. A000203, A000265, A003961, A064989, A161942, A342671, A348992, A349162, A349169 (gives odd k for which a(k) = A319627(k)).

Sequence in context: A104714 A085119 A010128 * A180133 A197419 A029764

Adjacent sequences: A348990 A348991 A348992 * A348994 A348995 A348996

KEYWORD

nonn,look

AUTHOR

Antti Karttunen, Nov 10 2021

STATUS

approved