A077657 Least number with exactly n consecutive successors, all having the same number of prime factors (counted with multiplicity).
1, 2, 33, 603, 602, 2522, 211673, 3405123, 3405122, 49799889, 202536181, 3195380868, 5208143601, 85843948321, 97524222465
Offset: 0
A077656 Numbers having a different number of prime factors as their successors (counted with multiplicity).
1, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 26, 28, 29, 30, 31, 32, 35, 36, 37, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83
Offset: 1
Keywords
Examples
20=2*2*5 and 20+1=21=3*7: A001222(20)<>A001222(21), therefore 20 is a term (A077655(20)=0).
Programs
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Mathematica
Position[Partition[PrimeOmega[Range[100]],2,1],?(#[[1]]!=#[[2]]&),{1}, Heads->False]//Flatten (* _Harvey P. Dale, Sep 19 2016 *)
A305234 Number of successors of n having the same value of A001221 as n.
0, 3, 2, 1, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 2, 1, 0, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 0, 4, 3, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 1
Offset: 1
Keywords
Examples
For n = 2: 3, 4 and 5 have the same number of distinct prime divisors as 2, but 6 does not, so a(2) = 3.
Programs
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PARI
a(n) = my(k=n+1, i=0); while(omega(k)==omega(n), i++; k++); i
Comments
Examples
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