A053026 -id:A053026 - cp's OEIS frontend

A380802 a(n) = log_2(A053026(n)).

0, 1, 2, 3, 4, 3, 2, 2, 2, 4, 3, 3, 3, 3, 3, 1, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 4, 4, 2, 4, 3, 4, 2, 2, 4, 2, 2, 1, 2, 4, 3, 4, 4, 2, 3, 3, 2, 3, 3, 4, 3, 3, 5, 5, 2, 5, 2, 2, 3, 2, 1, 5, 1, 3, 2, 3, 2, 3, 3, 3, 3, 1, 3, 3, 3, 5, 5, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 5, 3, 3, 1, 2, 1, 2, 3, 2, 2, 3, 3, 1, 3, 5, 2, 3, 2

Offset: 1

Amiram Eldar, Feb 04 2025

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A053026, A380803.

a[n_] := Log2[NestWhile[DivisorSigma[0, #] &, n!, # != 2^IntegerExponent[#, 2] &]]; Array[a, 100]

a(n) = {my(m = n!); while(1 << valuation(m, 2) != m, m = numdiv(m)); valuation(m, 2);}

A380803 a(n) is the least number k such that A380802(k) = n, or -1 if no such number exists.

Original entry on oeis.org

1, 2, 3, 4, 5, 53, 130, 212, 286, 563, 1215, 1279, 2835, 2434, 3930, 5011, 7031, 18217, 18692, 24218, 35317, 30986

Offset: 0

Amiram Eldar, Feb 04 2025

a(23) = 80200, a(26) = 112015, and there are no other terms below 158000.

Cf. A053026, A380802.

f[n_] := Log2[NestWhile[DivisorSigma[0, #] &, n!, # != 2^IntegerExponent[#, 2] &]]; (* A380802 *) seq[len_] := Module[{v = Table[0, {len}], c = 0, k = 1, i}, While[c < len, i = f[k] + 1; If[i <= len && v[[i]] == 0, c++; v[[i]] = k]; k++]; v]; seq[15]

f(n) = {my(m = n!); while(1 << valuation(m, 2) != m, m = numdiv(m)); valuation(m, 2);} \\ A380802
list(len) = {my(v = vector(len), c = 0, k = 1, i); while(c < len, i = f(k) + 1; if(i <= len && v[i] == 0, c++; v[i] = k); k++); v;}

cp's OEIS Frontend

A380802 a(n) = log_2(A053026(n)).

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