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A369204
Numbers m such that A034448(A188999(m)) = k*m for some k, where A034448 and A188999 are respectively the unitary and the bi-unitary sigma function.
2
1, 2, 8, 9, 10, 18, 24, 27, 30, 54, 165, 238, 288, 512, 656, 660, 864, 952, 1536, 1968, 2464, 2880, 4608, 4680, 13824, 14448, 14976, 16728, 19008, 19992, 23040, 29376, 60928, 152064, 155520, 172368, 279552, 474936, 746928, 1070592, 1114560, 1524096, 1703520
OFFSET
1,2
LINKS
EXAMPLE
A188999(18) = 4 * 10 = 40 and A034448(40) = 9 * 6 = 54 = 3 * 18, so 18 is a term with k = 3.
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) = (a034448(a188999(n))%n) == 0;
CROSSREFS
Cf. A038843 (analog for A034448(A034448(m))), A318175 (analog for A188999(A188999(m))).
Cf. A369205 (analog for A188999(A034448(m))).
Sequence in context: A037456 A277857 A360427 * A237280 A282636 A019511
KEYWORD
nonn
AUTHOR
Tomohiro Yamada, Jan 16 2024
STATUS
approved