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!)
 A324758 Heinz numbers of integer partitions containing no prime indices of the parts. 26
 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 16, 17, 19, 20, 21, 22, 23, 25, 27, 29, 31, 32, 33, 34, 35, 37, 40, 41, 43, 44, 46, 47, 49, 50, 51, 53, 57, 59, 61, 62, 63, 64, 65, 67, 68, 71, 73, 77, 79, 80, 81, 82, 83, 85, 87, 88, 89, 91, 92, 93, 94, 95, 97, 99, 100, 101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k). These could be described as anti-transitive numbers (cf. A290822), as they are numbers x such that if prime(y) divides x and prime(z) divides y, then prime(z) does not divide x. Also numbers n such that A003963(n) is coprime to n. LINKS EXAMPLE The sequence of terms together with their prime indices begins:    1: {}    2: {1}    3: {2}    4: {1,1}    5: {3}    7: {4}    8: {1,1,1}    9: {2,2}   10: {1,3}   11: {5}   13: {6}   16: {1,1,1,1}   17: {7}   19: {8}   20: {1,1,3}   21: {2,4}   22: {1,5}   23: {9}   25: {3,3}   27: {2,2,2} MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Select[Range[100], Intersection[primeMS[#], Union@@primeMS/@primeMS[#]]=={}&] CROSSREFS The subset version is A324741, with maximal case A324743. The strict integer partition version is A324751. The integer partition version is A324756. An infinite version is A324695. Cf. A000720, A001221, A001462, A007097, A056239, A112798, A276625, A289509, A290822, A304360, A306844, A324742, A324753, A324764. Sequence in context: A014122 A324759 A326621 * A305504 A316413 A316465 Adjacent sequences:  A324755 A324756 A324757 * A324759 A324760 A324761 KEYWORD nonn AUTHOR Gus Wiseman, Mar 17 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 March 29 02:19 EDT 2020. Contains 333104 sequences. (Running on oeis4.)