A277887 -id:A277887 - cp's OEIS frontend

A277888 Primes in A276573, the infinite trunk of least squares beanstalk.

3, 11, 43, 53, 59, 67, 83, 131, 139, 149, 173, 179, 227, 233, 251, 277, 283, 331, 347, 349, 419, 431, 491, 547, 557, 563, 571, 587, 617, 643, 659, 661, 683, 701, 733, 739, 743, 757, 821, 827, 907, 941, 947, 971, 1013, 1019, 1051, 1061, 1091, 1109, 1117, 1123, 1129, 1163, 1187, 1213, 1229, 1259, 1283, 1291, 1301, 1307, 1327, 1373, 1427, 1429, 1451, 1453

Offset: 1

Antti Karttunen, Nov 13 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..4248

Intersection of A000040 and A276573.

Cf. A277887, A277487, A278167.

(define (A277888 n) (A276573 (A277887 n)))

a(n) = A276573(A277887(n)).

A277886 If n is squarefree, a(n) = n, else a(n) = A000040(1+A277885(n)) * (n/(A249739(n)^2)).

Original entry on oeis.org

1, 2, 3, 3, 5, 6, 7, 6, 5, 10, 11, 9, 13, 14, 15, 12, 17, 10, 19, 15, 21, 22, 23, 18, 7, 26, 15, 21, 29, 30, 31, 24, 33, 34, 35, 27, 37, 38, 39, 30, 41, 42, 43, 33, 25, 46, 47, 36, 11, 14, 51, 39, 53, 30, 55, 42, 57, 58, 59, 45, 61, 62, 35, 48, 65, 66, 67, 51, 69, 70, 71, 54, 73, 74, 21, 57, 77, 78, 79, 60, 45

Offset: 1

Antti Karttunen, Nov 08 2016

nonn

If n has non-unitary prime divisors, then divide it by the square of the smallest of them and multiply by a single instance of the next larger prime.

This differs from related A097246 for the first time at n=16. For both sequences A097248 gives the eventual stable points reached when starting iterating from n.

			For n = 12 = 2*2*3, the smallest non-unitary prime divisor (and in this case the only one) is 2, thus we divide with 2^2 and multiply with the next larger prime 3, to get ((2^2 * 3)/(2^2))*3 = 3*3, thus a(12) = 9.
For n = 16 = 2^4, we divide two instances of 2 out and multiply by a single instance of 3 to get 2*2*3 = 12.

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000040, A048675, A097246, A097248, A249739, A277885, A277887, A277888, A277896.

Table[If[SquareFreeQ@ n, n, Prime[1 + PrimePi@ Min[Select[FactorInteger[n][[All, 1]], ! CoprimeQ[#, n/#] &] /. {} -> 0]] (n/If[SquareFreeQ@ n, 1, p = 2; While[! Divisible[n, p^2], p = NextPrime@ p]; p]^2)], {n, 81}] (* Michael De Vlieger, Nov 15 2016 *)

(define (A277886 n) (if (zero? (A277885 n)) n (* (A000040 (+ 1 (A277885 n))) (/ n (expt (A249739 n) 2)))))

If A277885(n) = 0 [when n is squarefree], then a(n) = n, otherwise a(n) = A000040(1+A277885(n)) * (n/(A249739(n)^2)).
Other identities. For all n >= 1:
A048675(a(n)) = A048675(n).

A278485 Positions of numbers that are one more than a prime in A276573, the infinite trunk of least squares beanstalk.

Original entry on oeis.org

1, 2, 3, 7, 9, 11, 12, 14, 18, 27, 30, 34, 38, 40, 47, 56, 58, 62, 70, 72, 73, 81, 86, 95, 97, 98, 106, 113, 115, 123, 131, 134, 139, 141, 153, 157, 159, 160, 162, 166, 167, 173, 176, 181, 183, 188, 195, 214, 216, 219, 223, 227, 233, 235, 244, 255, 259, 262, 270, 278, 286, 291, 296, 301, 307, 309, 315, 317, 326, 329, 346, 352, 355

Offset: 1

Antti Karttunen, Nov 25 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..5050

No common terms with A277887 after 1.

Cf. A010051, A276573, A278486, A278487.

cp's OEIS Frontend

A277888 Primes in A276573, the infinite trunk of least squares beanstalk.

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A277886 If n is squarefree, a(n) = n, else a(n) = A000040(1+A277885(n)) * (n/(A249739(n)^2)).

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A278485 Positions of numbers that are one more than a prime in A276573, the infinite trunk of least squares beanstalk.

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