The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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