A046756 Numbers k such that d(k)^4 divides k.

1, 625, 6561, 117649, 4100625, 31250000, 37515625, 73530625, 771895089, 1000000000, 2147483648, 6442450944, 10737418240, 15032385536, 23622320128, 25937424601, 27917287424, 32212254720, 33059881728, 36507222016, 40802189312, 45097156608, 49392123904

Offset

1,2

Comments

Proper subset of A033950, A046754 and A046755. Relatively prime terms are in the sequence together with their products like 73530625 or 771895089000000000.

2^31 is a term, as is every integer of the form 2^31*p, 2^31*p^3, and 2^31*p*q, where p and q are distinct odd primes; each of these has 32, 64, or 128 divisors. Of the first 10000 terms, 9609 are of one of those forms. Of the remaining 391 terms, 316 are of the form 2^8 * 3^17 * m, where m is 1, a prime > 3, or 5^4. - Jon E. Schoenfield, Aug 13 2022

Links

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000

Example

If k=625, d(k) = sigma(0,k) = 5. Its 4th power is 625, which divides k.

Mathematica

Select[ Range[ 1, 14500000 ], IntegerQ[ #/(DivisorSigma[ 0, # ])^2 ]& ]

Crossrefs

Cf. A033950, A046754, A046755.

Sequence in context: A250431 A046755 A016816 * A143026 A238700 A064781

Adjacent sequences: A046753 A046754 A046755 * A046757 A046758 A046759

Keyword

nonn

Author

Labos Elemer

Extensions

a(6)-a(20) from Donovan Johnson, Nov 30 2008

a(21)-a(23) from Donovan Johnson, Jun 08 2011

Status

approved