A275660 -id:A275660 - cp's OEIS frontend

A283757 Numbers n such that phi(n) = Sum_{j=1..k} d(n^j) for some k, where phi(n) is the Euler totient function of n and d(n) is the number of divisors of n.

1, 3, 8, 10, 18, 24, 30, 435, 485, 579, 678, 759, 1052, 1593, 3243, 3857, 3913, 4085, 4445, 4773, 4953, 5685, 6078, 6278, 6322, 6836, 7570, 9823, 10199, 10703, 12474, 12913, 12927, 14180, 14511, 14623, 16958, 17013, 17014, 17174, 17518, 17966, 18238, 19334, 19432

Offset: 1

Paolo P. Lava, Mar 16 2017

nonn

Values of k: {1, 1, 1, 1, 1, 1, 1, 4, 9, 9, 4, 5, 8, 9, 8, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 16, 9, 12, 12, 12, 4, 32, 12, 9, 12, 32, 12, 13, 12, 12, 12, 12, 12, 12, 9, ...}. - Michael De Vlieger, Mar 17 2017

			d(1052) + d(1052^2) + d(1052^3) + d(1052^4) + d(1052^5) + d(1052^6) + d(1052^7) + d(1052^8) = 524 = phi(1052).

Cf. A000005, A000010, A270389, A270713, A275660.

with(numtheory): P:=proc(q) local a,k,n; for n from 1 to q do a:=0; k:=0; while a

Select[Range@ 4000, Module[{k = 1, e = EulerPhi@ #, b}, While[Set[b, Sum[DivisorSigma[0, #^j], {j, k}]] < e, k++]; If[b == e, True, False]] &] (* Michael De Vlieger, Mar 17 2017 *)

A283758 Numbers whose sum of divisors is equal to the product of the number of divisors of their k first powers, for some k.

Original entry on oeis.org

5, 22, 23, 102, 110, 382, 497, 510, 517, 527, 719, 1436, 4509, 5039, 6906, 8426, 8786, 9051, 9598, 9741, 9951, 10011, 10505, 10795, 11005, 11431, 11501, 11891, 11995, 12121, 13661, 13777, 13891, 13919, 14101, 14129, 14141, 28780, 31636, 32572, 32756, 33028, 33356

Offset: 1

Paolo P. Lava, Mar 16 2017

nonn

Values of k: {2, 2, 3, 2, 2, 3, 3, 2, 3, 3, 5, 3, 3, 6, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, ...}. - Michael De Vlieger, Mar 17 2017

			sigma(382) = 576 and d(382) * d(382^2) * d(382^3) = 4 * 9 * 16 = 576;
sigma(9598) = 14400 and d(9598) * d(9598^2) * d(9598^3) * d(9598^4) = 4 * 9 * 16 * 25 = 14400.

Paolo P. Lava, Table of n, a(n) for n = 1..150

Cf. A000005, A000203, A270389, A270713, A275660, A283757, A283759.

with(numtheory): P:=proc(q) local a,k,n; for n from 1 to q do a:=1; k:=0; while a

Select[Range[2, 40000], Module[{k = 1, d = DivisorSigma[1, #], b}, While[Set[b, Product[DivisorSigma[0, #^j], {j, k}]] < d, k++]; If[b == d, True, False]] &] (* Michael De Vlieger, Mar 17 2017 *)

A283759 Numbers whose Euler totient function is equal to the product of the number of divisors of their k first powers, for some k.

Original entry on oeis.org

3, 7, 8, 10, 18, 24, 30, 57, 74, 344, 399, 494, 518, 629, 654, 679, 1154, 2408, 2989, 3048, 3175, 3458, 3789, 4218, 4578, 4890, 5022, 7668, 10602, 13720, 14647, 14701, 14837, 15613, 16133, 17563, 17945, 18335, 19608, 20195, 20358, 21243, 21336, 21423, 22083, 22503

Offset: 1

Paolo P. Lava, Mar 16 2017

nonn

Values of k: {1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 2, 3, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 3, 3, 3, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 4, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, ...}. - Michael De Vlieger, Mar 17 2017

			phi(629) = 576 and d(629) * d(629^2) * d(629^3) = 4 * 9 * 16= 576;
phi(14647) = 14400 and d(14647) * d(14647^2) * d(14647^3) * d(14647^4) = 4 * 9 * 16 * 25 = 14400.

Paolo P. Lava, Table of n, a(n) for n = 1..150

Cf. A000005, A000010, A270389, A270713, A275660, A283757, A283758.

with(numtheory): P:=proc(q) local a,k,n; for n from 1 to q do a:=1; k:=0; while a

Select[Range[2, 25000], Module[{k = 1, e = EulerPhi@ #, b}, While[Set[b, Product[DivisorSigma[0, #^j], {j, k}]] < e, k++]; If[b == e, True, False]] &] (* Michael De Vlieger, Mar 17 2017 *)

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A283757 Numbers n such that phi(n) = Sum_{j=1..k} d(n^j) for some k, where phi(n) is the Euler totient function of n and d(n) is the number of divisors of n.

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A283758 Numbers whose sum of divisors is equal to the product of the number of divisors of their k first powers, for some k.

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Keywords

Comments

Examples

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Crossrefs

Programs

Maple

Mathematica

A283759 Numbers whose Euler totient function is equal to the product of the number of divisors of their k first powers, for some k.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica