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A369169
Terms k of A025487 such that A000005(k) = A000688(k).
3
1, 16, 1296, 23040, 810000, 7257600, 16934400, 283852800, 1437004800, 1944810000, 13970880000, 30735936000, 232475443200, 852409958400, 1765360396800, 3269185920000, 7192209024000, 8029628006400, 28473963210000, 97893956160000, 181803061440000, 1086822696960000
OFFSET
1,2
COMMENTS
Since both A000005(k) and A000688(k) depend only on the prime signature of k (A124832), if k is a term of this sequence then every number m such that A046523(m) = k is a term of A369168.
From David A. Corneth, Jan 15 2024: (Start)
16 | a(n) for n > 1.
This sequence contains A002110(n)^4. (End)
REFERENCES
József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter II, page 73.
LINKS
Aleksandar Ivić, On the number of abelian groups of a given order and on certain related multiplicative functions, Journal of Number Theory, Vol. 16, No. 1 (1983), pp. 119-137.
EXAMPLE
16 is in the sequence as 16 has 5 divisors (1, 2, 4, 8, 16) and 5 factorizations into prime powers (16 = 2*8 = 4*4 = 2*2*4 = 2*2*2*2).
MATHEMATICA
lps = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]]; Select[lps, DivisorSigma[0, #] == FiniteAbelianGroupCount[#] &]
CROSSREFS
Intersection of A025487 and A369168.
Sequence in context: A163929 A072914 A007480 * A307814 A186420 A163395
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jan 15 2024
STATUS
approved