A274940 Let p^e be the largest prime power appearing in the factorization of sigma(n)/n into prime powers, where sigma = A000203. If p^e appears in the numerator of S(n)/n then a(n) = n*p, otherwise a(n) = n/p. Set a(1)=1.

1, 6, 6, 28, 1, 12, 14, 4, 117, 30, 1, 84, 1, 2, 30, 496, 1, 234, 1, 140, 42, 2, 1, 120, 775, 2, 9, 56, 1, 6, 62, 16, 66, 102, 70, 468, 1, 2, 3, 120, 1, 84, 1, 4, 585, 2, 1, 1488, 7, 1550, 3, 364, 1, 18, 5, 8, 3, 2, 1, 420, 1, 2, 819, 8128, 5, 6, 1, 4, 138, 210, 1, 936, 1, 2

Offset

1,2

References

Allan C. Wechsler, Posting to Math Fun Mailing List, July 16 2016.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

a(3) = 6 because sigma(3)/3 = 4/3; prime power factors are {2^2, 3^-1}; 2^2 is larger in magnitude thus p = 2 so 3 * 2 = 6.
a(4) = 28 because sigma(4)/4= 7/4; prime power factors are {2^2, 7^1}; 7 is larger in magnitude thus p = 7 so 4 * 7 = 28. - Michael De Vlieger, Jul 20 2016

Mathematica

Table[n #1^Sign[#2] & @@ Last@ FactorInteger@ First@ MaximalBy[#, Abs@ Log@ # &] &@ Map[#1^#2 & @@ # &, FactorInteger@ #] &[DivisorSigma[1, n]/n], {n, 74}] (* Michael De Vlieger, Jul 20 2016 *)

Prog

(PARI) cmpf(x, y) = f[x, 1]^abs(f[x, 2]) >= f[y, 1]^abs(f[y, 2]);
a(n) = if (n==1, 1, f = factor(sigma(n)/n); vf = vector(#f~, k, k); vsi = vecsort(vf, cmpf, 1); imax = vsi[#f~]; if (f[imax, 2] > 0, n*f[imax, 1], n/f[imax, 1])); \\ Michel Marcus, Jul 20 2016; corrected Jun 13 2022

Crossrefs

Cf. A000203, A274939, A274941.

Sequence in context: A339321 A241865 A243122 * A341548 A253066 A267651

Adjacent sequences: A274937 A274938 A274939 * A274941 A274942 A274943

Keyword

nonn

Author

N. J. A. Sloane, Jul 20 2016

Extensions

More terms from Michel Marcus, Jul 20 2016

Status

approved