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
KEYWORD
nonn
AUTHOR
Michel Marcus, Aug 20 2018
EXTENSIONS
More terms from Giovanni Resta, Aug 25 2018
STATUS
approved