A348949 -id:A348949 - cp's OEIS frontend

A348999 a(n) = A348929(A276086(n)), where A348929(n) = gcd(n, A003959(n)), A003959 is multiplicative with a(p^e) = (p+1)^e, and A276086 gives the prime product form of primorial base expansion of n.

1, 1, 1, 6, 1, 6, 1, 2, 3, 6, 3, 18, 1, 2, 3, 6, 9, 18, 1, 2, 3, 6, 9, 18, 1, 2, 3, 6, 9, 18, 1, 2, 1, 6, 1, 6, 1, 2, 3, 6, 3, 18, 1, 2, 3, 6, 9, 18, 1, 2, 3, 6, 9, 18, 1, 2, 3, 6, 9, 18, 1, 2, 1, 6, 1, 6, 1, 2, 3, 6, 3, 18, 1, 2, 3, 6, 9, 18, 1, 2, 3, 6, 9, 18, 1, 2, 3, 6, 9, 18, 1, 2, 1, 6, 1, 6, 1, 2, 3, 6, 3, 18

Offset: 0

Antti Karttunen, Nov 07 2021

After each primorial number (A002110), the apparent periodicity grows more complex.

Antti Karttunen, Table of n, a(n) for n = 0..11550
Index entries for sequences related to primorial base

Cf. A002110, A003959, A276086, A348929, A348949, A348950, A348998, A349000.

A348999(n) = { my(m1=1, m2=1, p=2); while(n, m1 *= (p^(n%p)); m2 *= ((1+p)^(n%p)); n = n\p; p = nextprime(1+p)); gcd(m1,m2); };

a(n) = A348929(A276086(n)).

a(n) = gcd(A276086(n), A348949(n)) = gcd(A276086(n), A348950(n)).

A348950 a(n) = A348507(A276086(n)), where A348507(n) = A003959(n) - n, A003959 is multiplicative with a(p^e) = (p+1)^e, and A276086 gives the prime product form of primorial base expansion of n.

Original entry on oeis.org

0, 1, 1, 6, 7, 30, 1, 8, 9, 42, 51, 198, 11, 58, 69, 282, 351, 1278, 91, 398, 489, 1842, 2331, 8118, 671, 2638, 3309, 11802, 15111, 50958, 1, 10, 11, 54, 65, 258, 13, 74, 87, 366, 453, 1674, 113, 514, 627, 2406, 3033, 10674, 853, 3434, 4287, 15486, 19773, 67194, 5993, 22354, 28347, 98166, 126513, 418914, 15, 94, 109

Offset: 0

Antti Karttunen, Nov 06 2021

Antti Karttunen, Table of n, a(n) for n = 0..11550
Index entries for sequences related to primorial base

Cf. A003959, A276086, A348507, A348949, A348999.

Cf. also A327860.

A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A348507(n) = (A003959(n) - n);
A348950(n) = A348507(A276086(n));

A348950(n) = { my(m1=1, m2=1, p=2); while(n, m1 *= (p^(n%p)); m2 *= ((1+p)^(n%p)); n = n\p; p = nextprime(1+p)); (m2-m1); };

a(n) = A348949(n) - A276086(n) = A348507(A276086(n)).

A348996 a(n) = usigma(A276086(n)), where usigma (A034448) is multiplicative with a(p^e) = (p^e)+1, and A276086 gives the prime product form of primorial base expansion of n.

Original entry on oeis.org

1, 3, 4, 12, 10, 30, 6, 18, 24, 72, 60, 180, 26, 78, 104, 312, 260, 780, 126, 378, 504, 1512, 1260, 3780, 626, 1878, 2504, 7512, 6260, 18780, 8, 24, 32, 96, 80, 240, 48, 144, 192, 576, 480, 1440, 208, 624, 832, 2496, 2080, 6240, 1008, 3024, 4032, 12096, 10080, 30240, 5008, 15024, 20032, 60096, 50080, 150240, 50, 150

Offset: 0

Antti Karttunen, Nov 07 2021

Index entries for sequences related to primorial base

Cf. A034448, A276086, A348997, A349000.

Cf. also A324653, A346470, A348949.

A348996(n) = { my(m=1, p=2); while(n, if(n%p, m *= (1+(p^(n%p)))); n = n\p; p = nextprime(1+p)); (m); };

a(n) = A034448(A276086(n)).

A348997 a(n) = A348733(A276086(n)), where A348733(n) = gcd(A003959(n), A034448(n)), and A276086 gives the prime product form of primorial base expansion of n.

Original entry on oeis.org

1, 3, 4, 12, 2, 6, 6, 18, 24, 72, 12, 36, 2, 6, 8, 24, 4, 12, 18, 54, 72, 216, 36, 108, 2, 6, 8, 24, 4, 12, 8, 24, 32, 96, 16, 48, 48, 144, 192, 576, 96, 288, 16, 48, 64, 192, 32, 96, 144, 432, 576, 1728, 288, 864, 16, 48, 64, 192, 32, 96, 2, 6, 8, 24, 4, 12, 12, 36, 48, 144, 24, 72, 4, 12, 16, 48, 8, 24, 36, 108, 144

Offset: 0

Antti Karttunen, Nov 07 2021

Antti Karttunen, Table of n, a(n) for n = 0..11550
Index entries for sequences related to primorial base

Cf. A003959, A034448, A276086, A348733, A348949, A348996.

Cf. also A346471 for similar construction. (Compare the scatter plots).

A348997(n) = { my(m1=1, m2=1, p=2); while(n, if(n%p, m1 *= ((1+p)^(n%p)); m2 *= (1+(p^(n%p)))); n = n\p; p = nextprime(1+p)); gcd(m1, m2); };

a(n) = A348733(A276086(n)) = gcd(A348949(n), A348996(n)).

cp's OEIS Frontend

A348999 a(n) = A348929(A276086(n)), where A348929(n) = gcd(n, A003959(n)), A003959 is multiplicative with a(p^e) = (p+1)^e, and A276086 gives the prime product form of primorial base expansion of n.

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Formula

A348950 a(n) = A348507(A276086(n)), where A348507(n) = A003959(n) - n, A003959 is multiplicative with a(p^e) = (p+1)^e, and A276086 gives the prime product form of primorial base expansion of n.

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Formula

A348996 a(n) = usigma(A276086(n)), where usigma (A034448) is multiplicative with a(p^e) = (p^e)+1, and A276086 gives the prime product form of primorial base expansion of n.

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Formula

A348997 a(n) = A348733(A276086(n)), where A348733(n) = gcd(A003959(n), A034448(n)), and A276086 gives the prime product form of primorial base expansion of n.

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Formula