A276528 -id:A276528 - cp's OEIS frontend

A277906 Least number with same prime signature as phi(n): a(n) = A046523(A000010(n)).

1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 6, 4, 12, 6, 8, 8, 16, 6, 12, 8, 12, 6, 6, 8, 12, 12, 12, 12, 12, 8, 30, 16, 12, 16, 24, 12, 36, 12, 24, 16, 24, 12, 30, 12, 24, 6, 6, 16, 30, 12, 32, 24, 12, 12, 24, 24, 36, 12, 6, 16, 60, 30, 36, 32, 48, 12, 30, 32, 12, 24, 30, 24, 72, 36, 24, 36, 60, 24, 30, 32, 24, 24, 6, 24

Offset: 1

Antti Karttunen, Nov 17 2016

nonn

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

Cf. A000010, A046523, A276528.

(define (A277906 n) (A046523 (A000010 n)))

a(n) = A046523(A000010(n)).

A296091 a(1) = 1 and for n > 1, the least number with the same prime signature as sigma(n)-1.

Original entry on oeis.org

1, 2, 2, 6, 2, 2, 2, 6, 12, 2, 2, 8, 2, 2, 2, 30, 2, 6, 2, 2, 2, 6, 2, 2, 30, 2, 6, 6, 2, 2, 2, 6, 2, 2, 2, 60, 2, 2, 6, 2, 2, 6, 2, 2, 6, 2, 2, 6, 24, 12, 2, 2, 2, 6, 2, 6, 2, 2, 2, 2, 2, 6, 2, 60, 2, 6, 2, 8, 6, 6, 2, 6, 2, 2, 6, 2, 6, 2, 2, 6, 120, 8, 2, 2, 2, 2, 6, 2, 2, 2, 6, 2, 2, 6, 6, 2, 2, 30, 6, 216, 2, 6, 2, 6, 2

Offset: 1

Antti Karttunen, Dec 07 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000203, A039653, A046523, A296211.

Cf. also A276528, A296092.

(define (A296091 n) (if (= 1 n) n (A046523 (+ -1 (A000203 n)))))

a(1) = 1; for n > 1, a(n) = A046523(A000203(n)-1) = A046523(A039653(n)).

A296092 Least number with the same prime signature as sigma(n)+1.

Original entry on oeis.org

2, 4, 2, 8, 2, 2, 4, 16, 6, 2, 2, 2, 6, 4, 4, 32, 2, 24, 6, 2, 6, 2, 4, 2, 32, 2, 2, 6, 2, 2, 6, 64, 4, 6, 4, 12, 6, 2, 6, 6, 2, 2, 12, 6, 2, 2, 4, 8, 6, 6, 2, 12, 6, 4, 2, 4, 16, 6, 2, 4, 12, 2, 30, 128, 6, 6, 6, 2, 2, 6, 2, 36, 12, 6, 8, 6, 2, 4, 16, 6, 6, 2, 6, 36, 2, 6, 4, 2, 6, 6, 2, 4, 6, 6, 4, 6, 12, 12, 2, 6, 2, 6, 30, 2, 2

Offset: 1

Antti Karttunen, Dec 07 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000203, A046523, A088580, A296212.

Cf. also A276528, A296076, A296078, A296085, A296091.

(define (A296092 n) (A046523 (+ 1 (A000203 n))))

a(n) = A046523(A088580(n)) = A046523(1+A000203(n)).

A083262 a(n) = sigma(A046523(n)), sum of divisors of the least number with the same prime signature as n.

Original entry on oeis.org

1, 3, 3, 7, 3, 12, 3, 15, 7, 12, 3, 28, 3, 12, 12, 31, 3, 28, 3, 28, 12, 12, 3, 60, 7, 12, 15, 28, 3, 72, 3, 63, 12, 12, 12, 91, 3, 12, 12, 60, 3, 72, 3, 28, 28, 12, 3, 124, 7, 28, 12, 28, 3, 60, 12, 60, 12, 12, 3, 168, 3, 12, 28, 127, 12, 72, 3, 28, 12, 72, 3, 195, 3, 12, 28, 28, 12, 72

Offset: 1

Labos Elemer, May 09 2003

nonn

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

Cf. A000203, A046523, A276528, A286360.

Table[DivisorSigma[1, Times @@ MapIndexed[Prime[First@ #2]^#1 &, Sort[FactorInteger[n][[All, -1]], Greater]] - Boole[n == 1]], {n, 78}] (* Michael De Vlieger, May 20 2017 *)

A046523(n) = my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]) \\ This function from Charles R Greathouse IV, Aug 17 2011
A083262(n) = sigma(A046523(n)); \\ Antti Karttunen, May 19 2017

Name clarified by Antti Karttunen, May 19 2017

cp's OEIS Frontend

A277906 Least number with same prime signature as phi(n): a(n) = A046523(A000010(n)).

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A296091 a(1) = 1 and for n > 1, the least number with the same prime signature as sigma(n)-1.

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A296092 Least number with the same prime signature as sigma(n)+1.

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A083262 a(n) = sigma(A046523(n)), sum of divisors of the least number with the same prime signature as n.

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