A327908
Nonprime squarefree numbers whose prime indices all have the same Omega (A001222) and the same sum of prime indices (A056239).
Original entry on oeis.org
1, 667, 2021, 4331, 5767, 7081, 7663, 11021, 11639, 12091, 13837, 15049, 20413, 23213, 26123, 31553, 34933, 35657, 35723, 37909, 37979, 38021, 41449, 42919, 44197, 45113, 51019, 53531, 58339, 63407, 66013, 70531, 72929, 73373, 73903, 75763, 83411, 87361, 90581
Offset: 1
The sequence of terms together with their prime indices begins:
1: {}
667: {9,10}
2021: {14,15}
4331: {18,20}
5767: {21,22}
7081: {21,25}
7663: {22,25}
11021: {27,28}
11639: {27,30}
12091: {28,30}
13837: {26,33}
15049: {26,35}
20413: {33,35}
23213: {34,39}
26123: {36,40}
31553: {34,49}
34933: {42,44}
35657: {42,45}
35723: {34,55}
37909: {39,49}
Equal sum of prime indices:
A327901Equal average of prime indices:
A327902
-
primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[10000],!PrimeQ[#]&&SquareFreeQ[#]&&SameQ@@PrimeOmega/@primeMS[#]&&SameQ@@Total/@primeMS/@primeMS[#]&]
A327901
Nonprime squarefree numbers whose prime indices all have the same sum of prime indices (A056239).
Original entry on oeis.org
1, 35, 143, 209, 247, 391, 493, 629, 667, 851, 901, 1073, 1219, 1333, 1457, 1537, 1891, 1961, 2021, 2201, 2623, 2717, 2759, 2867, 2993, 3053, 3239, 3337, 3827, 3977, 4061, 4183, 4223, 4331, 4387, 4633, 5429, 5633, 5767, 5959, 6157, 6191, 6319, 7081, 7093, 7519
Offset: 1
The sequence of terms together with their prime indices begins:
1: {}
35: {3,4}
143: {5,6}
209: {5,8}
247: {6,8}
391: {7,9}
493: {7,10}
629: {7,12}
667: {9,10}
851: {9,12}
901: {7,16}
1073: {10,12}
1219: {9,16}
1333: {11,14}
1457: {11,15}
1537: {10,16}
1891: {11,18}
1961: {12,16}
2021: {14,15}
2201: {11,20}
The version including primes and nonsquarefree numbers is
A326534.
The version for number of prime indices is
A327900.
The version for mean of prime indices is
A327902.
-
primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[1000],!PrimeQ[#]&&SquareFreeQ[#]&&SameQ@@Total/@primeMS/@primeMS[#]&];
A327902
Nonprime squarefree numbers whose prime indices all have the same average of prime indices (A326567/A326568).
Original entry on oeis.org
1, 21, 57, 115, 133, 145, 159, 371, 393, 399, 515, 535, 565, 667, 803, 869, 917, 933, 1007, 1067, 1113, 1963, 2021, 2095, 2157, 2165, 2177, 2249, 2285, 2315, 2363, 2369, 2461, 2489, 2599, 2705, 2751, 2839, 2987, 3021, 3103, 3277, 3335, 3707, 3859, 4331, 4367
Offset: 1
The sequence of terms together with their prime indices begins:
1: {}
21: {2,4}
57: {2,8}
115: {3,9}
133: {4,8}
145: {3,10}
159: {2,16}
371: {4,16}
393: {2,32}
399: {2,4,8}
515: {3,27}
535: {3,28}
565: {3,30}
667: {9,10}
803: {5,21}
869: {5,22}
917: {4,32}
933: {2,64}
1007: {8,16}
1067: {5,25}
The version including primes and nonsquarefree numbers is
A326536.
The version for number of prime indices is
A327900.
The version for sum of prime indices is
A327901.
-
primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[1000],!PrimeQ[#]&&SquareFreeQ[#]&&SameQ@@Mean/@primeMS/@primeMS[#]&];
Showing 1-3 of 3 results.
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