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A369205
Numbers m such that A188999(A034448(m)) = k*m for some k, where A034448 and A188999 are respectively the unitary and the bi-unitary sigma function.
2
1, 2, 9, 10, 15, 18, 21, 30, 40, 42, 60, 120, 288, 567, 630, 720, 756, 1023, 1134, 1428, 2046, 2160, 2268, 2520, 3024, 3276, 3570, 4092, 6048, 8184, 8925, 9240, 11424, 11550, 15345, 17850, 18144, 30690, 35700, 46200, 57120, 85680, 147312, 285600, 491040, 556920
OFFSET
1,2
LINKS
EXAMPLE
A034448(18) = 4 * 10 = 40 and A188999(40) = 15 * 6 = 90 = 5 * 18, so 18 is a term with k = 5.
PROG
(PARI) a034448(n) = {my(f, i, p, e); f=factor(n); for(i=1, #f~, p=f[i, 1]; e=f[i, 2]; f[i, 1]=p^e+1; f[i, 2]=1); factorback(f)};
a188999(n) = {my(f, i, p, e); f=factor(n); for(i=1, #f~, p=f[i, 1]; e=f[i, 2]; f[i, 1]=if(e%2, (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1)-p^(e/2)); f[i, 2]=1); factorback(f)};
isok(n) = (a188999(a034448(n))%n) == 0;
CROSSREFS
Cf. A038843 (analog for A034448(A034448(m))), A318175 (analog for A188999(A188999(m))).
Cf. A369204 (analog for A034448(A188999(m))).
Sequence in context: A051017 A078180 A058890 * A306998 A047468 A032929
KEYWORD
nonn
AUTHOR
Tomohiro Yamada, Jan 16 2024
STATUS
approved