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!)
 A316413 Heinz numbers of integer partitions whose length divides their sum. 78
 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 16, 17, 19, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 34, 37, 39, 41, 43, 46, 47, 49, 53, 55, 57, 59, 61, 62, 64, 67, 68, 71, 73, 78, 79, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 94, 97, 98, 99, 100, 101, 103, 105, 107, 109, 110 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS In other words, partitions whose average is an integer. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). LINKS R. J. Mathar, Table of n, a(n) for n = 1..1327 EXAMPLE Sequence of partitions whose length divides their sum begins (1), (2), (11), (3), (4), (111), (22), (31), (5), (6), (1111), (7), (8), (42), (51), (9), (33), (222), (411). MAPLE isA326413 := proc(n)     psigsu := A056239(n) ;     psigle := numtheory[bigomega](n) ;     if modp(psigsu, psigle) = 0 then         true;     else         false;     end if; end proc: n := 1: for i from 2 to 3000 do     if isA326413(i) then         printf("%d %d\n", n, i);         n := n+1 ;     end if; end do: # R. J. Mathar, Aug 09 2019 MATHEMATICA Select[Range[2, 100], Divisible[Total[Cases[FactorInteger[#], {p_, k_}:>k*PrimePi[p]]], PrimeOmega[#]]&] CROSSREFS Cf. A056239, A067538, A074761, A143773, A237984, A289508, A289509, A290103, A296150, A298423, A316428, A316431. Sequence in context: A326621 A324758 A305504 * A316465 A004764 A128649 Adjacent sequences:  A316410 A316411 A316412 * A316414 A316415 A316416 KEYWORD nonn AUTHOR Gus Wiseman, Jul 02 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 26 15:49 EDT 2021. Contains 346294 sequences. (Running on oeis4.)