A361419 -id:A361419 - cp's OEIS frontend

A361420 a(n) is the unique number m such that A126168(m) = A361419(n).

1, 6, 8, 15, 21, 52, 58, 82, 106, 118, 268, 158, 356, 1264, 1296, 388, 202, 214, 226, 130, 508, 524, 1936, 160, 138, 298, 692, 2608, 358, 3088, 288, 446, 454, 466, 932, 478, 432, 348, 1792, 538, 562, 578, 586, 12032, 1268, 748, 20736, 1348, 694, 706, 26368, 544, 758

Offset: 1

Amiram Eldar, Mar 11 2023

nonn

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

Cf. A126168, A361419.

Similar sequences: A357313, A357325.

f[p_, e_] := Module[{b = IntegerDigits[e, 2]}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; is[1] = 0; is[n_] := Times @@ f @@@ FactorInteger[n] - n;
seq[max_] := Module[{v = s = Table[0, {max}], i}, Do[i = is[k] + 1; If[i <= max, v[[i]]++; s[[i]] = k], {k, 1, max^2}]; s[[Position[v, 1] // Flatten]]];
seq[500]

s(n) = {my(f = factor(n), b); prod(i=1, #f~, b = binary(f[i, 2]); prod(k=1, #b, if(b[k], f[i, 1]^(2^(#b-k)) + 1, 1))) - n; }
lista(nmax) = {my(v = w = vector(nmax+1)); for(k=1, nmax^2, i = s(k) + 1; if(i <= nmax+1, v[i] += 1; w[i] = k)); for(i = 1, nmax+1, if(v[i] == 1, print1(w[i], ", "))); }

A126168(a(n)) = A361419(n).

A372742 Numbers k such that there is a unique number m for which the sum of the aliquot coreful divisors of m (A336563) is k.

Original entry on oeis.org

2, 3, 5, 7, 11, 12, 13, 17, 18, 19, 23, 24, 29, 31, 36, 37, 41, 43, 47, 53, 56, 59, 61, 67, 71, 73, 79, 80, 83, 84, 89, 96, 97, 98, 101, 103, 107, 109, 112, 113, 127, 131, 135, 137, 139, 140, 149, 150, 151, 156, 157, 163, 167, 173, 179, 181, 191, 193, 197, 198

Offset: 1

Amiram Eldar, May 12 2024

nonn

A coreful divisor d of n is a divisor that is divisible by every prime that divides n (see also A307958).
Numbers k such that A372739(k) = 1.
The corresponding values of m are in A372743.
Includes all prime numbers.

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

Cf. A336563, A372739, A372743.
A000040 is a subsequence.
Similar sequences: A057709, A357324, A361419.

f[p_, e_] := (p^(e + 1) - 1)/(p - 1) - 1; s[1] = 0; s[n_] := Times @@ f @@@ FactorInteger[n] - n; seq[max_] := Module[{v = Table[0, {max}], i}, Do[i = s[k]; If[1 <= i <= max, v[[i]]++], {k, 1, max^2}]; Position[v, 1] // Flatten]; seq[200]

s(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^(f[i, 2] + 1) - 1)/(f[i, 1] -1) - 1) - n;}
lista(nmax) = {my(v = vector(nmax), i); for(k=1, nmax^2, i = s(k); if(i > 0 && i <= nmax, v[i]++)); for(k = 1, nmax, if(v[k] == 1, print1(k, ", ")));}

a(n) = A336563(A372743(n)).

cp's OEIS Frontend

A361420 a(n) is the unique number m such that A126168(m) = A361419(n).

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