A274939 Numbers n with property that in the factorization of sigma(n)/n into a product of prime powers, the largest prime power is found in the denominator (here sigma(n) is the sum of the divisors of n, A000203(n)).

5, 8, 11, 13, 14, 17, 19, 22, 23, 26, 27, 29, 30, 32, 37, 38, 39, 41, 43, 44, 46, 47, 49, 51, 53, 54, 55, 56, 57, 58, 59, 61, 62, 65, 66, 67, 68, 71, 73, 74, 76, 78, 79, 82, 83, 86, 87, 88, 89, 92, 94, 95, 96, 97, 98, 101, 102, 103, 104, 107, 108, 109, 111, 113

Offset

1,1

References

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

Links

Table of n, a(n) for n=1..64.

Example

List of [n, factorization of S(n)/n], with terms satisfying the condition marked with ***:
[1, 1]
[2, (3)/(2)]
[3, (2)^2/(3)]
[4, (7)/(2)^2]
[5, (2)*(3)/(5)] ***
[6, (2)]
[7, (2)^3/(7)]
[8, (3)*(5)/(2)^3] ***
[9,  (13)/(3)^2]
[10, (3)^2/(5)]
[11, (2)^2*(3)/(11)] ***
[12, (7)/(3)]
[13, (2)*(7)/(13)] ***
[14, (2)^2*(3)/(7)] ***
[15, (2)^3/(5)]
[16, (31)/(2)^4]
[17, (2)*(3)^2/(17)] ***
[18, (13)/(2)/(3)]
...

Prog

(PARI) cmpf(x, y) = f[x, 1]^abs(f[x, 2]) >= f[y, 1]^abs(f[y, 2]);
isok(n) = f = factor(sigma(n)/n); vf = vector(#f~, k, k); vsi = vecsort(vf, cmpf, 1); f[vsi[#f~], 2] < 0; \\ Michel Marcus, Jul 20 2016

Crossrefs

Cf. A000203 (sigma), A274940, A274941.

sigma(n)/n = A017665/A017666.

Sequence in context: A104275 A053726 A246371 * A173977 A161537 A248634

Adjacent sequences: A274936 A274937 A274938 * A274940 A274941 A274942

Keyword

nonn

Author

N. J. A. Sloane, Jul 19 2016

Extensions

More terms from Michel Marcus, Jul 20 2016

Status

approved