A329026 -id:A329026 - cp's OEIS frontend

A251362 Numbers n such that n is the concatenation of distinct prime factors of phi(n), in increasing order.

25, 235741, 23517131, 274873357929, 2357131984859

Offset: 1

Jahangeer Kholdi, Dec 03 2014

Numbers n such that n = A084317(A000010(n)). - Michel Marcus, Dec 06 2014

			25 is in the sequence since phi(25)=2^2*5,
235741 is in the sequence since phi(235741)=2^4*3^2*5*7*41,
23517131 is in the sequence since phi(23517131)=2^7*3*5^2*17*131.

Cf. A000010, A000040, A084317, A251360, A251361, A251363, A329026.

a251362[n_Integer] := Rest@ Select[Range[n], # ==
FromDigits[Flatten@IntegerDigits[First@Transpose@FactorInteger[EulerPhi[#]]]] &]; a251362[10^6] (* Michael De Vlieger, Dec 03 2014 *)

a(4)-a(5) from Max Alekseyev, Feb 11 2025

A329025 If n = Product (p_j^k_j) then a(n) = concatenation (pi(p_j)), where pi = A000720.

Original entry on oeis.org

0, 1, 2, 1, 3, 12, 4, 1, 2, 13, 5, 12, 6, 14, 23, 1, 7, 12, 8, 13, 24, 15, 9, 12, 3, 16, 2, 14, 10, 123, 11, 1, 25, 17, 34, 12, 12, 18, 26, 13, 13, 124, 14, 15, 23, 19, 15, 12, 4, 13, 27, 16, 16, 12, 35, 14, 28, 110, 17, 123, 18, 111, 24, 1, 36, 125, 19, 17, 29, 134

Offset: 1

Ilya Gutkovskiy, Nov 02 2019

Concatenate of indices of distinct prime factors of n, in increasing order.

			a(60) = a(2^2 * 3 * 5) = a(prime(1)^2 * prime(2) * prime(3)) = 123.

Ilya Gutkovskiy, Scatter plot of a(n) up to n=100000
Index entries for sequences computed from indices in prime factorization

Cf. A000720, A037916, A080695, A084317, A127668, A304038, A329026.

a[n_] := FromDigits[Flatten@IntegerDigits@(PrimePi[#[[1]]] & /@ FactorInteger[n])]; Table[a[n], {n, 1, 70}]

a(prime(n)^k) = n for k > 0.

cp's OEIS Frontend

A251362 Numbers n such that n is the concatenation of distinct prime factors of phi(n), in increasing order.

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