A330999 -id:A330999 - cp's OEIS frontend

A331000 Unitary Ruth-Aaron numbers: numbers k such that A008475(k) = A008475(k+1).

5, 77, 714, 948, 2491, 2996, 3450, 4293, 5405, 6669, 9125, 10807, 13869, 14587, 16932, 17346, 19511, 19967, 23323, 26642, 27104, 31931, 33019, 37925, 41124, 43616, 48635, 52554, 55499, 58077, 58695, 79248, 80837, 86088, 89979, 95709, 98644, 99163, 108458, 117467

Offset: 1

Amiram Eldar, Jan 05 2020

nonn

A variation of Ruth-Aaron numbers with unitary prime-power divisors instead of prime divisors.

			5 is a term since A008475(5) = A008475(6) = 5.

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

Cf. A006145, A039752, A008475, A330999.

s[1] = 0; s[n_] := Plus @@ (Power @@@ FactorInteger[n]); seq = {}; s1 = 0; Do[s2 = s[n]; If[s1 == s2, AppendTo[seq, n - 1]]; s1 = s2, {n, 2, 10^5}]; seq

A333802 Numbers k such that A181894(k)+1 = A181894(k+1).

Original entry on oeis.org

2, 3, 4, 16, 20, 35, 143, 152, 208, 256, 650, 1624, 2232, 4233, 4345, 5368, 8099, 9424, 11024, 11919, 12099, 14905, 18424, 20220, 21716, 22194, 24335, 25592, 26123, 27390, 30457, 34945, 38180, 40425, 51992, 52206, 52947, 56563, 63712, 65536, 67123, 71154, 71284

Offset: 1

Amiram Eldar, Apr 05 2020

nonn

A variation of A064111 and A228126 with "Fermi-Dirac primes" (or infinitary components) instead of prime divisors.

			4 is a term since A181894(4) + 1 = 4 + 1 = 5 = A181894(5).

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

Cf. A006145, A039752, A050376, A064111, A181894, A228126, A330999, A333801.

f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], 1])); s[1] = 0; s[n_] := Plus @@ (Flatten @ (f @@@ FactorInteger[n])); seq = {}; s1 = 0; Do[s2 = s[n]; If[s1 + 1 == s2, AppendTo[seq, n - 1]]; s1 = s2, {n, 2, 10^5}]; seq

cp's OEIS Frontend

A331000 Unitary Ruth-Aaron numbers: numbers k such that A008475(k) = A008475(k+1).

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