A072510 -id:A072510 - cp's OEIS frontend

A072327 Numbers k such that k^2 is a term of A072510.

1, 8, 12, 27, 32, 45, 63, 125, 175, 225, 243, 275, 325, 343, 425, 475, 539, 560, 575, 637, 720, 833, 931, 1127, 1225, 1331, 1421, 1519, 1573, 1813, 2009, 2057, 2107, 2197, 2240, 2299, 2303, 2783, 2816, 2873, 3025, 3125, 3211, 3328, 3509, 3751, 3887, 4352, 4477

Offset: 1

Vladimir Baltic, Aug 04 2002

nonn

Numbers of the form p^(m*(4m-1)) and p^(m*(4m+1)) are terms of the sequence, where p is prime. p^2*q are terms of the sequence, where p and q are prime and p^2 > q > p.

Complement of A072497 in the positive integers. - Robert Israel, Dec 10 2024

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A072497, A072498, A072510.

filter:= proc(n) local s, F, d, p;
  s:= n^2;
  F:= sort(convert(numtheory:-divisors(s), list));
  p:= 1:
  for d in F do
    p:= p*d;
    if p > s then return false
    elif p = s then return true
    fi
  od;
end proc:
select(filter, [$1..5000]); # Robert Israel, Dec 10 2024

More terms from Sean A. Irvine, Sep 23 2024

A072498 n is not equal to the product of the k smallest divisors of n for any k.

Original entry on oeis.org

4, 9, 12, 16, 18, 20, 25, 28, 32, 36, 42, 44, 45, 48, 49, 50, 52, 54, 60, 63, 66, 68, 72, 75, 76, 78, 80, 81, 84, 88, 90, 92, 96, 98, 99, 100, 102, 104, 108, 110, 112, 114, 116, 117, 121, 124, 126, 128, 130, 132, 136, 138, 140, 147, 148, 150, 152, 153, 156, 160, 162

Offset: 1

Vladimir Baltic, Aug 03 2002

nonn

Positive integers not included in A072510. Sequence includes all squares of primes.

			Divisors of 384 are 1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384. Partial products are: 1=1, 1*2=2, 1*2*3=6, 1*2*3*4=24, 1*2*3*4*6=144, 1*2*3*4*6*8=1152 and so 384 (144<384<1152) is not in A072510.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A072510.

filter:= proc(n) local F,d,p;
  F:= sort(convert(numtheory:-divisors(n),list));
  p:= 1:
  for d in F do
    p:= p*d;
    if p > n then return true
    elif p = n then return false
    fi
  od;
end proc:
select(filter, [$1..1000]); # Robert Israel, Sep 28 2016

Select[Range[200],!MemberQ[FoldList[Times,1,Divisors[#]],#]&] (* Harvey P. Dale, Jun 18 2013 *)

Edited by Robert Israel, Sep 28 2016

A072497 Numbers k such that k^2 is a member of A072498.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78

Offset: 1

Vladimir Baltic, Aug 04 2002

nonn

p^m are members of the sequence, where p is prime and m different from k(4k-1) and k(4k+1) (spatially all primes, p^1).

Complement of A072327 in the positive integers. - Robert Israel, Dec 10 2024

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A072498, A072327, A072510.

filter:= proc(n) local s, F, d, p;
  s:= n^2;
  F:= sort(convert(numtheory:-divisors(s), list));
  p:= 1:
  for d in F do
    p:= p*d;
    if p > s then return true
    elif p = s then return false
    fi
  od;
end proc:
select(filter, [$1..100]); # Robert Israel, Dec 10 2024

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A072327 Numbers k such that k^2 is a term of A072510.

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A072498 n is not equal to the product of the k smallest divisors of n for any k.

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A072497 Numbers k such that k^2 is a member of A072498.

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Maple