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URL: https://oeis.org/A380459

⇱ A380459 - OEIS

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A380459
a(n) = Product_{d|n} A276086(n/d)^A349394(d).
24
1, 2, 2, 12, 2, 18, 2, 1296, 48, 54, 2, 1620, 2, 30, 108, 25194240, 2, 4050, 2, 131220, 60, 270, 2, 12150000, 576, 150, 3317760, 67500, 2, 33750, 2, 142818689064960000, 540, 1350, 180, 2050312500, 2, 750, 300, 1195742250000, 2, 281250, 2, 82012500, 26244000, 6750, 2, 92264062500000000, 1280, 13668750, 2700, 42187500, 2
OFFSET
1,2
FORMULA
For n >= 1, A276085(a(n)) = A003415(n).
From Antti Karttunen, Feb 01 2026: (Start)
For squarefree n, a(n) = Product_{p|n, p prime} A276086(n/p).
Iff n is in A380468, then a(n) = A327859(n).
(End)
PROG
(PARI)
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A349394(n) = { my(p=0, e); if((e=isprimepower(n, &p)), p^(e-1), 0); };
A380459(n) = { my(m=1); fordiv(n, d, m *= A276086(d)^A349394(n/d)); (m); };
CROSSREFS
Cf. A003415, A276085, A276086, A349394, A380460 (rgs-transform).
Cf. A327859 [= A392878(a(n))], A368915 [= A377868(a(n))], A380479 [= A001222(a(n))], A380480 [= A051903(a(n))], A380528 [= A129252(a(n))].
Cf. A380468 [k such that a(k) is in A048103], A380475, A380476 (its subsequences), A380470 [squarefree k such that a(k) is not in A048103].
Cf. also A329350, A329380.
Sequence in context: A076976 A291757 A286464 * A058044 A223453 A285729
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 31 2025
STATUS
approved