login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A316437 Take the integer partition with Heinz number n, divide all parts by the GCD of the parts, then take the Heinz number of the resulting partition. 5
1, 2, 2, 4, 2, 6, 2, 8, 4, 10, 2, 12, 2, 14, 15, 16, 2, 18, 2, 20, 6, 22, 2, 24, 4, 26, 8, 28, 2, 30, 2, 32, 33, 34, 35, 36, 2, 38, 10, 40, 2, 42, 2, 44, 45, 46, 2, 48, 4, 50, 51, 52, 2, 54, 55, 56, 14, 58, 2, 60, 2, 62, 12, 64, 6, 66, 2, 68, 69, 70, 2, 72, 2, 74, 75, 76, 77, 78, 2, 80, 16, 82, 2, 84, 85, 86, 22, 88, 2, 90, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
This sequence is idempotent, meaning a(a(n)) = a(n) for all n.
All terms belong to A289509.
LINKS
Wikipedia, Idempotence
MATHEMATICA
f[n_]:=If[n==1, 1, With[{pms=Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]}, Times@@Prime/@(pms/GCD@@pms)]];
Table[f[n], {n, 100}]
PROG
(PARI) A316437(n) = if(1==n, 1, my(f = factor(n), pis = apply(p -> primepi(p), f[, 1]~), es = f[, 2]~, g = gcd(pis)); factorback(vector(#f~, k, prime(pis[k]/g)^es[k]))); \\ Antti Karttunen, Aug 06 2018
CROSSREFS
Sequence in context: A320389 A046801 A348717 * A137502 A318885 A307088
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 03 2018
EXTENSIONS
More terms from Antti Karttunen, Aug 06 2018
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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)