A349750 -id:A349750 - cp's OEIS frontend

A349749 Odd numbers k for which the 3-adic valuation of sigma(k) is equal to the 3-adic valuation of k, where sigma is the sum of divisors function.

1, 7, 13, 15, 19, 25, 31, 33, 37, 43, 61, 67, 69, 73, 79, 87, 91, 97, 103, 105, 109, 121, 123, 127, 133, 139, 141, 147, 151, 153, 157, 163, 175, 177, 181, 193, 195, 199, 211, 217, 223, 229, 231, 241, 247, 249, 259, 271, 277, 283, 285, 289, 301, 303, 307, 313, 325, 331, 337, 339, 343, 349, 367, 373, 375, 379, 393, 397

Offset: 1

Antti Karttunen, Nov 30 2021

nonn

Odd numbers for which sigma (A000203) preserves the 3-adic valuation (A007949).

Cf. A000203, A007949, A329963, A349750, A349751.

Cf. A349169, A349752, A349755 (subsequences).

Select[Range[1, 400, 2], IntegerExponent[DivisorSigma[1, #], 3] == IntegerExponent[#, 3] &] (* Amiram Eldar, Dec 01 2021 *)

isA349749(n) = ((n%2)&&valuation(sigma(n),3)==valuation(n,3));

A349752 Odd numbers k for which the sigma(k) == -k (mod 3) and sigma(k) preserves the 3-adic valuation of k.

Original entry on oeis.org

7, 13, 15, 19, 31, 33, 37, 43, 61, 67, 69, 73, 79, 87, 97, 103, 105, 109, 123, 127, 139, 141, 147, 151, 153, 157, 163, 175, 177, 181, 193, 195, 199, 211, 223, 229, 231, 241, 249, 271, 277, 283, 285, 303, 307, 313, 325, 331, 337, 339, 349, 367, 373, 375, 379, 393, 397, 409, 411, 421, 429, 433, 439, 447, 457, 463

Offset: 1

Antti Karttunen, Nov 30 2021

nonn

Incidentally, of the 37 known terms of A228059, all of which are multiples of three, only 15 (less than half) satisfy this condition.

Intersection of A349749 and A349751.

Cf. A000203, A007949, A010872, A074941, A228059, A329963, A349750.

Select[Range[1, 463, 2], Divisible[(s = DivisorSigma[1, #]) + #, 3] && IntegerExponent[s, 3] == IntegerExponent[#, 3] &] (* Amiram Eldar, Dec 01 2021 *)

isA349752(n) = ((n%2) && (0==(sigma(n)+n)%3) && valuation(sigma(n), 3)==valuation(n, 3));

A349751 Odd numbers k such that sigma(k) == -k (mod 3), where sigma is the sum of divisors function.

Original entry on oeis.org

7, 13, 15, 19, 31, 33, 37, 43, 45, 51, 61, 67, 69, 73, 79, 87, 97, 99, 103, 105, 109, 123, 127, 135, 139, 141, 147, 151, 153, 157, 159, 163, 165, 175, 177, 181, 193, 195, 199, 207, 211, 213, 223, 229, 231, 241, 249, 255, 261, 267, 271, 277, 283, 285, 297, 303, 307, 313, 315, 321, 325, 331, 337, 339, 345, 349, 357

Offset: 1

Antti Karttunen, Nov 30 2021

nonn

Odd numbers k for which A155085(k) is a multiple of 3.

			7 is present as 7 mod 3 = +1, while sigma(7) = 8, and 8 mod 3 = 2, i.e., -1.
45 is present as 45 mod 3 = 0, while sigma(45) = 78, and 78 mod 3 = 0 as well.

Cf. A000203, A010872, A074941, A155085, A349750.

Cf. A349752 (intersection with A349749).

Select[Range[1, 360, 2], Divisible[DivisorSigma[1, #] + #, 3] &] (* Amiram Eldar, Dec 01 2021 *)

isA349751(n) = ((n%2)&&0==(sigma(n)+n)%3);

cp's OEIS Frontend

A349749 Odd numbers k for which the 3-adic valuation of sigma(k) is equal to the 3-adic valuation of k, where sigma is the sum of divisors function.

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A349752 Odd numbers k for which the sigma(k) == -k (mod 3) and sigma(k) preserves the 3-adic valuation of k.

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Mathematica

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A349751 Odd numbers k such that sigma(k) == -k (mod 3), where sigma is the sum of divisors function.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI