A051279 -id:A051279 - cp's OEIS frontend

A063080 Numbers k such that k/d(k) is prime, where d(k) is the number of divisors of k.

8, 9, 12, 18, 24, 40, 56, 60, 84, 88, 104, 132, 136, 152, 156, 184, 204, 228, 232, 248, 276, 296, 328, 344, 348, 372, 376, 424, 444, 472, 488, 492, 516, 536, 564, 568, 584, 632, 636, 664, 708, 712, 732, 776, 804, 808, 824, 852, 856, 872, 876, 904, 948, 996

Offset: 1

Jason Earls, Aug 05 2001

If p is an odd prime, then 8*p is a term. - Amiram Eldar, Apr 17 2024

			k = 18: 18/d(18) = 3 a prime.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

Cf. A000005, A039819, A036762, A051278, A051279, A051280, A036763, A033950.

Select[Range[1000],PrimeQ[#/DivisorSigma[0,#]]&] (* Harvey P. Dale, Sep 01 2014 *)

ok(m)={my(d=numdiv(m)); m%d==0 && isprime(m/d)}

A078541 Refactorable numbers x, such that quotient x/A000005(x) equals a power of 2.

Original entry on oeis.org

1, 2, 8, 12, 36, 80, 96, 128, 288, 448, 2560, 6144, 11264, 18432, 32768, 53248, 57344, 245760, 737280, 1114112, 2621440, 4980736, 22020096, 23068672, 25165824, 66060288, 75497472, 96468992, 436207616, 939524096, 1258291200, 1811939328, 2147483648, 3774873600

Offset: 1

Labos Elemer, Dec 04 2002

nonn

This sequence is infinite since it contains all the terms of A058891. Also, 3*2^A083329(k) is a term for all k >= 1. - Amiram Eldar, Jan 27 2025

			a(6)=80: tau(80)=10, quotient=80/10=8=2^3; certain powers of 2 do not appear as quotient, like 64, 1024, 16384.

Donovan Johnson, Table of n, a(n) for n = 1..100

Cf. A000005, A033950, A036763, A051278, A051279, A051280, A058891, A083329.

Do[s=n/DivisorSigma[0, n]; If[IntegerQ[Log[2, s]], Print[{n, s, n/s}]], {n, 1, 1000000000}]

isok(k) = my(r = k/numdiv(k)); denominator(r) == 1 && r >> valuation(r, 2) == 1; \\ Amiram Eldar, Jan 27 2025

a(n)/tau(a(n))=2^s with some s, tau()=A000005().

a(29)-a(34) from Donovan Johnson, Jun 04 2011

cp's OEIS Frontend

A063080 Numbers k such that k/d(k) is prime, where d(k) is the number of divisors of k.

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