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A365432
a(n) = A156552(A364502(n)), where A364502(n) = A005940(n) / gcd(n, A005940(n)), and A156552 is the inverse of offset-0 version of Doudna-sequence A005940.
3
0, 0, 0, 0, 0, 0, 6, 0, 8, 0, 10, 0, 12, 6, 6, 0, 16, 8, 18, 0, 4, 10, 22, 0, 24, 12, 12, 6, 28, 6, 30, 0, 32, 16, 34, 8, 36, 18, 18, 0, 40, 4, 42, 10, 20, 22, 46, 0, 48, 24, 24, 12, 52, 12, 22, 6, 56, 28, 58, 6, 60, 30, 14, 0, 64, 32, 66, 16, 68, 34, 70, 8, 72, 36, 16, 18, 12, 18, 78, 0, 80, 40, 82, 4, 40, 42, 42, 10
OFFSET
1,7
LINKS
FORMULA
For all n >= 1, a(n) <= n-1 and A341520(a(n), A365430(n)) = n-1.
PROG
(PARI)
A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A364502(n) = { my(u=A005940(n)); (u / gcd(n, u)); };
CROSSREFS
Cf. A005940, A364500, A341520, A365430, A365431 (rgs-transform).
Sequence in context: A201521 A011393 A066362 * A279929 A244812 A083680
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 07 2023
STATUS
approved