The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A325756 A number k belongs to the sequence if k = 1 or k is divisible by its prime shadow A181819(k) and the quotient k/A181819(k) also belongs to the sequence. 7
 1, 2, 12, 336, 360, 45696, 52416, 75600, 22665216, 31804416, 42928704, 77792400, 92610000, 164656800, 174636000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS We define the prime shadow A181819(k) 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. LINKS Table of n, a(n) for n=1..15. EXAMPLE The sequence of terms together with their prime indices begins: 1: {} 2: {1} 12: {1,1,2} 336: {1,1,1,1,2,4} 360: {1,1,1,2,2,3} 45696: {1,1,1,1,1,1,1,2,4,7} 52416: {1,1,1,1,1,1,2,2,4,6} 75600: {1,1,1,1,2,2,2,3,3,4} MATHEMATICA red[n_] := If[n == 1, 1, Times @@ Prime /@ Last /@ FactorInteger[n]]; suQ[n_]:=n==1||Divisible[n, red[n]]&&suQ[n/red[n]]; Select[Range, suQ] PROG (PARI) ps(n) = my(f=factor(n)); prod(k=1, #f~, prime(f[k, 2])); \\ A181819 isok(k) = {if ((k==1), return(1)); my(p=ps(k)); ((k % p) == 0) && isok(k/p); } \\ Michel Marcus, Jan 09 2021 CROSSREFS Cf. A181819, A182857, A290689, A290822, A323014, A324843, A325702, A325706, A325708, A325755. Sequence in context: A156518 A012727 A296622 * A181142 A088229 A060596 Adjacent sequences: A325753 A325754 A325755 * A325757 A325758 A325759 KEYWORD nonn,more AUTHOR Gus Wiseman, May 19 2019 EXTENSIONS a(9)-a(15) from Amiram Eldar, Jan 09 2021 STATUS approved

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

Last modified June 2 02:01 EDT 2023. Contains 363081 sequences. (Running on oeis4.)