A364960 Numbers k such that A005940(k) is either k itself or its descendant in Doudna-tree, A005940.

1, 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 24, 25, 32, 40, 45, 48, 49, 64, 80, 96, 128, 160, 192, 256, 320, 384, 512, 640, 768, 1024, 1280, 1536, 2048, 2560, 3072, 4096, 5120, 6144, 8192, 10240, 12288, 16384, 20480, 24576, 32768, 40131, 40960, 49152, 50575, 65536, 79625, 81920, 98304, 131072, 163840, 196608, 262144, 327680

Offset: 1

Author

Antti Karttunen, Aug 14 2023

Keywords

• nonn

Comments

Numbers k such that A252464(k) is equal to A364569(k).

Crossrefs

Positions of 0's in A364570.

Cf. A252464, A364569.

Subsequences: A029747, A364961 (odd terms).

Programs

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A252463(n) = if(!(n%2),n/2,A064989(n));
isA364960(n) = { my(k=A005940(n)); while(k>n, k = A252463(k)); (k==n); };

PARI

Abincompreflen(n, m) = { my(x=binary(n), y=binary(m), u=min(#x, #y)); for(i=1, u, if(x[i]!=y[i], return(i-1))); (u); };
A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A364569(n) = Abincompreflen(A156552(n), (n-1));
A061395(n) = if(n>1, primepi(vecmax(factor(n)[, 1])), 0);
A252464(n) = if(1==n,0,(bigomega(n) + A061395(n) - 1));
isA364960(n) = (A252464(n)==A364569(n));