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!)
A325042 Heinz numbers of integer partitions whose product of parts is one fewer than their sum. 14
4, 6, 10, 14, 18, 22, 26, 34, 38, 46, 58, 60, 62, 74, 82, 86, 94, 106, 118, 122, 134, 142, 146, 158, 166, 168, 178, 194, 202, 206, 214, 216, 218, 226, 254, 262, 274, 278, 298, 302, 314, 326, 334, 346, 358, 362, 382, 386, 394, 398, 400, 422, 446, 454, 458, 466 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1) * ... * prime(y_k), so these are numbers whose product of prime indices (A003963) is one fewer than their sum of prime indices (A056239).
LINKS
FORMULA
A003963(a(n)) = A056239(a(n)) - 1.
a(n) = 2 * A301987(n).
EXAMPLE
The sequence of terms together with their prime indices begins:
4: {1,1}
6: {1,2}
10: {1,3}
14: {1,4}
18: {1,2,2}
22: {1,5}
26: {1,6}
34: {1,7}
38: {1,8}
46: {1,9}
58: {1,10}
60: {1,1,2,3}
62: {1,11}
74: {1,12}
82: {1,13}
86: {1,14}
94: {1,15}
106: {1,16}
118: {1,17}
122: {1,18}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1000], Times@@primeMS[#]==Total[primeMS[#]]-1&]
CROSSREFS
Sequence in context: A310584 A165779 A287375 * A137860 A184335 A243428
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 25 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 05:43 EDT 2024. Contains 371264 sequences. (Running on oeis4.)