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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)).
2
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.
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 19 2016
EXTENSIONS
More terms from Michel Marcus, Jul 20 2016
STATUS
approved