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A325755 Numbers n divisible by their prime shadow A181819(n). 9
1, 2, 9, 12, 18, 36, 40, 60, 84, 112, 120, 125, 132, 156, 180, 204, 225, 228, 250, 252, 276, 280, 336, 348, 352, 360, 372, 396, 440, 441, 444, 450, 468, 492, 516, 520, 540, 560, 564, 600, 612, 636, 675, 680, 684, 708, 732, 760, 804, 828, 832, 840, 852, 876 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

We define the prime shadow A181819(n) to be the product of primes indexed by the exponents in the prime factorization of n. For example, 90 = prime(1)*prime(2)^2*prime(3) has prime shadow prime(1)*prime(2)*prime(1) = 12.

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions containing their multiset of multiplicities as a submultiset (counted by A325702).

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

The sequence of terms together with their prime indices begins:

     1: {}

     2: {1}

     9: {2,2}

    12: {1,1,2}

    18: {1,2,2}

    36: {1,1,2,2}

    40: {1,1,1,3}

    60: {1,1,2,3}

    84: {1,1,2,4}

   112: {1,1,1,1,4}

   120: {1,1,1,2,3}

   125: {3,3,3}

   132: {1,1,2,5}

   156: {1,1,2,6}

   180: {1,1,2,2,3}

   204: {1,1,2,7}

   225: {2,2,3,3}

   228: {1,1,2,8}

   250: {1,3,3,3}

   252: {1,1,2,2,4}

MATHEMATICA

red[n_]:=If[n==1, 1, Times@@Prime/@Last/@FactorInteger[n]];

Select[Range[100], Divisible[#, red[#]]&]

CROSSREFS

Cf. A181819, A182857, A290689, A290822, A323014, A324843, A325702, A325706, A325708, A325756.

Sequence in context: A050855 A031070 A225547 * A324570 A109297 A048768

Adjacent sequences:  A325752 A325753 A325754 * A325756 A325757 A325758

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 19 2019

STATUS

approved

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Last modified July 24 23:25 EDT 2021. Contains 346273 sequences. (Running on oeis4.)