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

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A338552 Non-powers of primes whose prime indices have a common divisor > 1. 3
 21, 39, 57, 63, 65, 87, 91, 111, 115, 117, 129, 133, 147, 159, 171, 183, 185, 189, 203, 213, 235, 237, 247, 259, 261, 267, 273, 299, 301, 303, 305, 319, 321, 325, 333, 339, 351, 365, 371, 377, 387, 393, 399, 417, 427, 441, 445, 453, 477, 481, 489, 497, 507 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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. Also Heinz numbers of non-constant, non-relatively prime partitions. The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), giving a bijective correspondence between positive integers and integer partitions. LINKS FORMULA Equals A024619 /\ A318978. Complement of A000961 \/ A289509. EXAMPLE The sequence of terms together with their prime indices begins: 21: {2,4} 183: {2,18} 305: {3,18} 39: {2,6} 185: {3,12} 319: {5,10} 57: {2,8} 189: {2,2,2,4} 321: {2,28} 63: {2,2,4} 203: {4,10} 325: {3,3,6} 65: {3,6} 213: {2,20} 333: {2,2,12} 87: {2,10} 235: {3,15} 339: {2,30} 91: {4,6} 237: {2,22} 351: {2,2,2,6} 111: {2,12} 247: {6,8} 365: {3,21} 115: {3,9} 259: {4,12} 371: {4,16} 117: {2,2,6} 261: {2,2,10} 377: {6,10} 129: {2,14} 267: {2,24} 387: {2,2,14} 133: {4,8} 273: {2,4,6} 393: {2,32} 147: {2,4,4} 299: {6,9} 399: {2,4,8} 159: {2,16} 301: {4,14} 417: {2,34} 171: {2,2,8} 303: {2,26} 427: {4,18} MATHEMATICA Select[Range[100], !(#==1||PrimePowerQ[#]||GCD@@PrimePi/@First/@FactorInteger[#]==1)&] CROSSREFS A318978 allows prime powers, counted by A018783, with complement A289509. A327685 allows nonprime prime powers. A338330 is the coprime instead of relatively prime version. A338554 counts the partitions with these Heinz numbers. A338555 is the complement. A000740 counts relatively prime compositions. A000961 lists powers of primes, with complement A024619. A051424 counts pairwise coprime or singleton partitions. A108572 counts nontrivial periodic partitions, with Heinz numbers A001597. A291166 ranks relatively prime compositions, with complement A291165. A302696 gives the Heinz numbers of pairwise coprime partitions. A327516 counts pairwise coprime partitions, with Heinz numbers A302696. Cf. A000005, A000837, A007916, A056239, A112798, A289508, A302569, A302796, A318716, A327658, A328867, A328677, A338331, A338553. Sequence in context: A102478 A221048 A182297 * A339002 A339004 A270667 Adjacent sequences: A338549 A338550 A338551 * A338553 A338554 A338555 KEYWORD nonn AUTHOR Gus Wiseman, Nov 03 2020 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 December 6 10:38 EST 2022. Contains 358630 sequences. (Running on oeis4.)