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A318182 Numbers m such that A049417(A049417(m)) = k*m for some k where A049417 is the infinitary sigma function. 3
1, 2, 8, 9, 10, 15, 18, 24, 30, 60, 720, 1020, 4080, 8925, 14688, 14976, 16728, 17850, 35700, 36720, 37440, 66912, 71400, 285600, 308448, 381888, 428400, 602208, 636480, 763776, 856800, 1321920, 1505520, 3011040, 3084480, 21679488, 22276800, 30844800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(86) > 3*10^11. All the prime factors of the first 85 terms belong to the set {2, 3, 5, 7, 11, 13, 17, 41, 43, 257}. - Giovanni Resta, Aug 25 2018

Like in A019278, here there are many instances where if x is a term, then A049417(x) is also a term.

Additionally, there exist longer chains of 3 or 4 elements like:

- 8 (3), 15 (4), 24 (5), 60 (6);

- 9 (2), 10 (3), 18 (4), 30 (5);

- 31615920 (4), 50585472 (5), 126463680 (6), 252927360 (12);

- 963407296051200 (16), 3134896756992000 (17), 15414516736819200 (18);

- 3541951043592192 (5), 8854877608980480 (6), 17709755217960960 (12), 53129265653882880 (20);

- 4829933241262080 (11), 17709755217960960 (12), 53129265653882880 (20);

  7871002319093760 (9), 26564632826941440 (10), 70839020871843840 (13), 265646328269414400 (14).

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..85 (first 58 terms from Tomohiro Yamada)

Tomohiro Yamada, Infinitary superperfect numbers, Annales Mathematicae et Informaticae, 47 (2017) pp. 211-218. See Table 1.

Michel Marcus, Unexhaustive list of terms

PROG

(PARI) a049417(n) = {my(b, f=factorint(n)); prod(k=1, #f[, 2], b = binary(f[k, 2]); prod(j=1, #b, if(b[j], 1+f[k, 1]^(2^(#b-j)), 1))); }

isok(n) = frac(a049417(a049417(n))/n) == 0;

CROSSREFS

Cf. A049417 (infinitary sigma).

Cf. A019278 (analog for sigma), A318175 (analog for bi-unitary sigma).

Sequence in context: A167450 A050569 A318175 * A047469 A283774 A037456

Adjacent sequences:  A318179 A318180 A318181 * A318183 A318184 A318185

KEYWORD

nonn

AUTHOR

Michel Marcus, Aug 20 2018

EXTENSIONS

More terms from Giovanni Resta, Aug 25 2018

STATUS

approved

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Last modified April 4 20:37 EDT 2020. Contains 333229 sequences. (Running on oeis4.)