A138394 -id:A138394 - cp's OEIS frontend

A140752 Indices of elements of A005179 that belong to A134865 (in order of their appearance in A134865). The sorted version of this sequence is given by A138394.

1, 2, 3, 4, 6, 8, 9, 10, 16, 20, 24, 30, 48, 60, 64, 72, 80, 84, 100, 108, 126, 192, 162, 224, 189, 384, 448, 512, 576, 672, 11520

Offset: 1

Max Alekseyev, May 26 2008

Cf. A000005, A005179, A134865, A138394, A140753.

a(n) = A000005(A134865(n))

a(31)=11520 from Ray Chandler, Jun 30 2008

A134865 Numbers k meeting the following criterion: if k is a multiple of d, then it is also a multiple of the smallest number with same number of divisors as d.

Original entry on oeis.org

1, 2, 4, 6, 12, 24, 36, 48, 120, 240, 360, 720, 2520, 5040, 7560, 10080, 15120, 20160, 45360, 50400, 100800, 332640, 352800, 665280, 705600, 4324320, 8648640, 17297280, 21621600, 43243200, 13492656777600

Offset: 1

J. Lowell, Jan 29 2008

Note that this is not a subsequence of A002182: 100800 is in this sequence but not in A002182. - J. Lowell, Feb 22 2008
A subset of A005179. - Max Alekseyev, May 19 2008
A number k is in this sequence iff for every divisor d of k, A005179(A000005(d)) (= A140635(d)) is also a divisor of k. So the question of the finiteness of this sequence is closely related to the form of the elements of A005179. - Max Alekseyev, May 19 2008, May 20 2008
Rearrangement of this sequence, forming a subsequence of A005179, is given by A140753. Corresponding indices of elements of A005179 are given by A138394 and A140752. - Max Alekseyev, May 26 2008
A subsequence of A007416 which is a subsequence of A025487, so every term is primally tight and even (after the first term). Thus if d is a divisor of a term, then the least integer with the same prime signature as d (=A046523(d)) is also a divisor. So only the divisors that are in A025487 need be tested. - Ray Chandler
a(32) > 8*10^25 if it exists. - David A. Corneth, Dec 10 2021

			60 is a multiple of 30 with 8 divisors, but not of 24 (the smallest number with 8 divisors) so 60 is not a term of this sequence.

Cf. A000005, A005179, A007416, A138394, A140752, A140753.

a = {}; For[n = 1, n < 10000, n++, b = Divisors[n]; c = 1; For[i = 1, i < Length[b] + 1, i++, j = 1; While[Length[Divisors[j]] < Length[Divisors[b[[i]]]], j++ ]; If[ ! Mod[n, j] == 0, c = 0]]; If[c == 1, AppendTo[a, n]]]; a (* Stefan Steinerberger, Feb 05 2008 *)

isA134865(n)={ n%2 & return(n==1); fordiv(n, d, bigomega(d)>1 || next; nd=numdiv(d); for(k=4, d, numdiv(k)==nd || next; n%k & return; break)); 1 }
for(n=1,10^7,if(isA134865(n),print1(n,", "))); \\ R. J. Mathar, May 17 2008

a(n) = A005179(A140752(n)). - Max Alekseyev, May 26 2008

More terms from Stefan Steinerberger, Feb 05 2008
More terms from J. Lowell, Feb 22 2008
a(22)-a(30) from Don Reble, May 17 2008
a(31)=13492656777600 from Ray Chandler, Jun 30 2008

A140753 Subsequence of elements of A005179 that appear in A134865.

Original entry on oeis.org

1, 2, 4, 6, 12, 24, 36, 48, 120, 240, 360, 720, 2520, 5040, 7560, 10080, 15120, 20160, 45360, 50400, 100800, 352800, 705600, 332640, 665280, 4324320, 8648640, 17297280, 21621600, 43243200, 13492656777600

Offset: 1

Max Alekseyev, May 26 2008

Rearrangement of elements of A134865 in order of their appearance in A005179. Hence A134865 represents a sorted variant of this sequence.

Cf. A000005, A005179, A134865, A138394, A140752.

a(n) = A005179(A138394(n))

a(31)=13492656777600 from Ray Chandler, Jun 30 2008

cp's OEIS Frontend

A140752 Indices of elements of A005179 that belong to A134865 (in order of their appearance in A134865). The sorted version of this sequence is given by A138394.

Views

Author

Keywords

Crossrefs

Formula

Extensions

A134865 Numbers k meeting the following criterion: if k is a multiple of d, then it is also a multiple of the smallest number with same number of divisors as d.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A140753 Subsequence of elements of A005179 that appear in A134865.

Views

Author

Keywords

Comments

Crossrefs

Formula

Extensions